[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"public-settings":3,"content:materi:fungsi-kuadrat":11,"public-catalog":219},{"features.tutoring.enabled":4,"sections.subjects.enabled":5,"sections.pricing.enabled":5,"sections.teachers.enabled":5,"sections.testimonials.enabled":4,"sections.faqs.enabled":5,"bankSoal.enabled":5,"site.maintenance":4,"whatsapp.number":6,"brand.name":7,"brand.tagline":8,"contact.email":9,"contact.address":10},false,true,"6285156084435","MyFismat","Platform belajar Matematika, Fisika, dan Pemrograman untuk SD, SMP, SMA, dan Kuliah","support@myfismat.com","Indonesia",{"id":12,"type":13,"slug":14,"title":15,"excerpt":16,"coverUrl":17,"status":18,"publishedAt":19,"featured":5,"subjectId":20,"blocks":21,"seoTitle":17,"seoDescription":17,"readingMinutes":106,"order":107,"createdAt":108,"updatedAt":108,"subject":109,"levels":114,"topics":119,"tags":123,"author":17,"resolved":124,"related":147},"demo-v2-m-matematika-sma-1","MATERIAL","fungsi-kuadrat","Fungsi Kuadrat: Grafik, Titik Puncak, dan Contoh Soal","Fungsi kuadrat f(x) = ax² + bx + c: pengaruh a, b, c pada grafik, rumus titik puncak, sumbu simetri, diskriminan, dan contoh soal nilai maksimum.",null,"PUBLISHED","2026-10-08T23:58:22.894Z","cmuzbyhdg000471r9l54yc9ia",[22,27,34,38,42,46,50,54,58,63,70,74,78,84,88,92,96,100],{"id":23,"data":24,"type":26},"s1-1",{"markdown":25},"**Fungsi kuadrat** adalah fungsi berbentuk $f(x)=ax^2+bx+c$ dengan $a\\ne0$, dan grafiknya berupa **parabola**. Parabola terbuka ke atas jika $a>0$ dan ke bawah jika $a\u003C0$, sedangkan $c$ adalah titik potongnya dengan sumbu $y$. Titik balik parabola disebut **titik puncak**, dengan koordinat $x_p=-\\frac{b}{2a}$ dan $y_p=-\\frac{D}{4a}$, di mana $D=b^2-4ac$ adalah diskriminan.","text",{"id":28,"data":29,"type":33},"s1-2",{"title":30,"variant":31,"markdown":32},"Rumus penting fungsi kuadrat","info","Titik puncak: $\\left(-\\dfrac{b}{2a},\\,-\\dfrac{D}{4a}\\right)$ dengan $D=b^2-4ac$\n\nSumbu simetri: $x=-\\dfrac{b}{2a}$\n\nBentuk puncak: $f(x)=a(x-x_p)^2+y_p$","callout",{"id":35,"data":36,"type":26},"s2-1",{"markdown":37},"## Apa Itu Fungsi Kuadrat?\n\nFungsi kuadrat memasangkan setiap $x$ dengan satu nilai $ax^2+bx+c$. Pangkat tertinggi variabelnya **dua**. Fungsi ini dipelajari di SMA kelas 10 dan muncul di banyak masalah: lintasan bola, luas maksimum taman, dan keuntungan maksimum penjualan.\n\nFungsi kuadrat dapat ditulis dalam tiga bentuk, masing-masing memperlihatkan informasi berbeda:\n\n| Bentuk | Rumus | Informasi yang langsung terbaca |\n|---|---|---|\n| Umum | $ax^2+bx+c$ | titik potong sumbu $y$: $(0,c)$ |\n| Faktor | $a(x-x_1)(x-x_2)$ | akar atau titik potong sumbu $x$ |\n| Puncak | $a(x-x_p)^2+y_p$ | titik puncak $(x_p,y_p)$ |",{"id":39,"data":40,"type":26},"s3-1",{"markdown":41},"## Pengaruh Nilai a, b, dan c pada Grafik\n\n- **Nilai $a$** menentukan arah buka dan kelebaran. $a>0$ terbuka ke atas (punya nilai minimum), $a\u003C0$ terbuka ke bawah (punya nilai maksimum). Makin besar $|a|$, parabola makin sempit.\n- **Nilai $b$** bersama $a$ menentukan letak sumbu simetri. Jika $a$ dan $b$ bertanda sama, puncak ada di kiri sumbu $y$; jika berbeda tanda, puncak ada di kanan.\n- **Nilai $c$** adalah titik potong dengan sumbu $y$, karena $f(0)=c$.",{"id":43,"data":44,"type":26},"s4-1",{"markdown":45},"## Rumus Titik Puncak dan Sumbu Simetri\n\nParabola simetris terhadap garis tegak $x=x_p$. Dua titik dengan jarak sama dari sumbu simetri mempunyai nilai $y$ sama. Rumusnya:\n\n$$x_p=-\\frac{b}{2a},\\qquad y_p=f(x_p)=-\\frac{b^2-4ac}{4a}$$\n\nCara paling aman adalah menghitung $x_p$ dulu, lalu substitusi ke fungsi untuk mendapat $y_p$. Bentuk puncak juga dapat diperoleh dengan **melengkapkan kuadrat**: $x^2-6x+5=(x-3)^2-9+5=(x-3)^2-4$, jadi puncaknya $(3,-4)$.",{"id":47,"data":48,"type":26},"s5-1",{"markdown":49},"## Diskriminan dan Titik Potong Sumbu X\n\nTitik potong sumbu $x$ diperoleh dari $f(x)=0$. Banyaknya ditentukan oleh **diskriminan** $D=b^2-4ac$:\n\n- $D>0$: memotong sumbu $x$ di dua titik berbeda;\n- $D=0$: **menyinggung** sumbu $x$ di satu titik (puncak tepat di sumbu $x$);\n- $D\u003C0$: tidak memotong sumbu $x$.\n\nJika $a>0$ dan $D\u003C0$, grafik selalu di atas sumbu $x$ (**definit positif**). Jika $a\u003C0$ dan $D\u003C0$, grafik selalu di bawah sumbu $x$ (**definit negatif**).",{"id":51,"data":52,"type":26},"s6-1",{"markdown":53},"## Rumus ABC untuk Titik Potong Sumbu X\n\nJika fungsi sulit difaktorkan, pakai **rumus ABC**:\n\n$$x_{1,2}=\\frac{-b\\pm\\sqrt{D}}{2a}$$\n\nContohnya $x^2-4x+1=0$: $D=16-4=12$, sehingga $x=\\frac{4\\pm\\sqrt{12}}{2}=2\\pm\\sqrt3$. Kedua akar berjarak sama, yaitu $\\sqrt3$, dari sumbu simetri $x=2$. Pola ini selalu terjadi karena rumus ABC dapat ditulis $x=-\\frac b{2a}\\pm\\frac{\\sqrt D}{2a}$.",{"id":55,"data":56,"type":26},"s7-1",{"markdown":57},"## Cara Menggambar Grafik Fungsi Kuadrat\n\n1. Tentukan arah buka dari tanda $a$.\n2. Cari titik potong sumbu $y$: $(0,c)$.\n3. Cari titik potong sumbu $x$ dengan pemfaktoran atau rumus ABC, jika $D\\ge0$.\n4. Cari titik puncak dan sumbu simetri.\n5. Gambar titik-titik itu, lalu hubungkan dengan kurva mulus yang simetris.",{"id":59,"data":60,"type":33},"visual-guide",{"title":61,"variant":31,"markdown":62},"Eksplorasi visual","- Model awal $a=1$, $b=0$, $c=0$ menampilkan $y=x^2$. Cek titik $(0,0)$, $(1,1)$, dan $(-1,1)$.\n- Atur $b=-2$ dan $c=-3$ dengan $a$ tetap 1 untuk memperoleh $y=x^2-2x-3$. Temukan akar $(-1,0)$ dan $(3,0)$ serta puncak $(1,-4)$.\n- Ubah hanya $c$ naik-turun. Apa yang terjadi pada grafik? (Grafik bergeser tegak.)\n- Ubah $a$ menjadi $-1$. Arah buka parabola berubah. Hitung ulang puncaknya dengan $x_p=-\\frac{b}{2a}$, karena perubahan $a$ juga menggeser puncak.\n- Cari nilai $c$ yang membuat parabola $y=x^2-2x+c$ tepat menyinggung sumbu $x$. (Petunjuk: diskriminan nol.)",{"id":64,"data":65,"type":69},"visual",{"height":66,"assetId":67,"caption":68},520,"demo-v2-asset-quadratic","Grafik fungsi kuadrat: puncak dan akar","interactive",{"id":71,"data":72,"type":26},"s8-1",{"markdown":73},"## Contoh Soal Fungsi Kuadrat dan Pembahasan\n\n### Contoh 1: Akar dan puncak\n\nDiberikan $f(x)=x^2-2x-3$.\n\n1. Faktorkan: $(x-3)(x+1)=0$, jadi akarnya $x=3$ dan $x=-1$.\n2. $x_p=-\\frac{-2}{2(1)}=1$ dan $y_p=f(1)=1-2-3=-4$. Puncak $(1,-4)$.\n3. Cek simetri: akar berjarak 2 dari $x=1$, dan $f(0)=f(2)=-3$.\n\n### Contoh 2: Luas taman maksimum\n\nTaman persegi panjang dipagari 20 m. Jika lebarnya $x$, panjangnya $10-x$, dan luasnya $A(x)=x(10-x)=-x^2+10x$.\n\n1. $a=-1\u003C0$, jadi ada nilai maksimum.\n2. $x_p=-\\frac{10}{2(-1)}=5$, dan $A(5)=25$.\n3. Luas maksimum $25\\text{ m}^2$ saat taman berbentuk persegi 5 m × 5 m.\n\n### Contoh 3: Menyusun fungsi dari puncak\n\nParabola berpuncak $(2,-1)$ dan melalui $(0,3)$. Tulis $f(x)=a(x-2)^2-1$. Substitusi $(0,3)$: $3=4a-1$, jadi $a=1$. Fungsinya $f(x)=(x-2)^2-1=x^2-4x+3$.\n\n### Contoh 4: Grafik menyinggung sumbu x\n\nTentukan $c$ agar grafik $y=x^2-2x+c$ menyinggung sumbu $x$. Syaratnya $D=0$: $(-2)^2-4(1)(c)=0$, sehingga $4-4c=0$ dan $c=1$. Fungsinya $y=(x-1)^2$, berpuncak tepat di $(1,0)$.",{"id":75,"data":76,"type":26},"s9-1",{"markdown":77},"## Kesalahan yang Sering Terjadi",{"id":79,"data":80,"type":33},"s9-2",{"title":81,"variant":82,"markdown":83},"Tanda di dalam kurung","warning","Puncak $(x-1)^2-4$ adalah $(1,-4)$, **bukan** $(-1,-4)$. Kuadrat bernilai nol saat $x=1$.",{"id":85,"data":86,"type":26},"s9-3",{"markdown":87},"- Menentukan arah buka dari tanda $c$, padahal yang menentukan adalah $a$.\n- Lupa tanda minus pada $-\\frac b{2a}$.\n- Pada soal cerita, lupa memeriksa bahwa nilai optimum berada di domain yang masuk akal.",{"id":89,"data":90,"type":26},"s10-1",{"markdown":91},"## Ringkasan\n\n- $f(x)=ax^2+bx+c$, grafik parabola; $a$ menentukan arah buka.\n- Puncak $\\left(-\\frac b{2a},-\\frac D{4a}\\right)$; sumbu simetri $x=-\\frac b{2a}$.\n- $D>0$ dua titik potong, $D=0$ menyinggung, $D\u003C0$ tidak memotong sumbu $x$.\n- Nilai maksimum\u002Fminimum fungsi adalah $y_p$.",{"id":93,"data":94,"type":26},"s11-1",{"markdown":95},"## Materi Terkait\n\nFungsi kuadrat adalah langkah berikutnya setelah [persamaan garis lurus](\u002Fmateri\u002Fpersamaan-garis-lurus). Pertumbuhan yang jauh lebih cepat dari kuadrat dibahas di [eksponen dan logaritma](\u002Fmateri\u002Feksponen-dan-logaritma). Di kuliah, puncak parabola dicari dengan [turunan](\u002Fmateri\u002Fdefinisi-turunan-limit): gradien garis singgung di puncak bernilai nol.",{"id":97,"data":98,"type":26},"sources",{"markdown":99},"## Sumber belajar\n\n- [OpenStax Algebra and Trigonometry 2e — Quadratic Functions](https:\u002F\u002Fopenstax.org\u002Fbooks\u002Falgebra-and-trigonometry-2e\u002Fpages\u002F5-1-quadratic-functions)\n\nPenjelasan dan contoh disusun ulang untuk materi ini; sumber dapat dibuka untuk belajar lebih lanjut.",{"id":101,"data":102,"type":105},"practice",{"title":103,"questionSetId":104},"Latihan soal Fungsi Kuadrat","demo-v2-p-matematika-sma-1","quiz",4,0,"2026-10-08T23:58:22.895Z",{"id":20,"slug":110,"name":111,"color":112,"icon":113},"matematika","Matematika","#8B5CF6","sigma",[115],{"id":116,"slug":117,"name":118},"cmuzbyhdb000271r9up0bfli4","sma","SMA",[120],{"id":121,"slug":14,"name":122,"subjectId":20},"demo-v2-topic-matematika-sma-1","Fungsi Kuadrat",[],{"assets":125,"videos":140,"questionSets":141},{"demo-v2-asset-quadratic":126},{"id":67,"slug":127,"kind":128,"title":68,"description":129,"url":17,"posterUrl":17,"config":130,"subject":139},"grafik-fungsi-kuadrat","GRAPH_2D","Ubah a, b, dan c pada y = ax² + bx + c untuk melihat perubahan parabola, titik puncak, dan akar.",{"a":131,"b":107,"c":107,"xMax":132,"xMin":133,"yMax":132,"yMin":133,"angle":134,"model":135,"omega":136,"slope":131,"speed":137,"gravity":138,"amplitude":131,"intercept":107},1,5,-5,45,"quadratic",2,20,9.8,{"id":20,"slug":110,"name":111},{},{"demo-v2-p-matematika-sma-1":142},{"id":104,"slug":143,"title":144,"mode":145,"description":146,"questionCount":132,"durationMinutes":17},"latihan-soal-fungsi-kuadrat","Latihan Soal Fungsi Kuadrat","PRACTICE","5 soal Fungsi Kuadrat (Matematika SMA) lengkap dengan pembahasan langkah demi langkah dan alasan pilihan yang 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soal.","2026-10-08T23:58:23.070Z","2026-10-08T23:58:23.072Z",{"id":20,"slug":110,"name":111,"color":112,"icon":113},[183],{"id":169,"slug":170,"name":171},[185],{"id":186,"slug":176,"name":187,"subjectId":20},"demo-v2-topic-matematika-kuliah-3","Vektor 3D dan Dot Product",[],{"id":190,"type":13,"slug":191,"title":192,"excerpt":193,"coverUrl":17,"status":18,"publishedAt":194,"featured":4,"readingMinutes":106,"order":131,"updatedAt":195,"subject":196,"levels":197,"topics":199,"tags":203,"author":17},"demo-v2-m-matematika-kuliah-2","integral-tentu","Integral Tentu: Rumus, Luas, dan Volume Benda Putar","Integral tentu dan teorema dasar kalkulus, sifat-sifatnya, luas daerah antara kurva, volume benda putar metode cakram dan kulit tabung, plus contoh soal.","2026-10-08T23:58:23.034Z","2026-10-08T23:58:23.037Z",{"id":20,"slug":110,"name":111,"color":112,"icon":113},[198],{"id":169,"slug":170,"name":171},[200],{"id":201,"slug":191,"name":202,"subjectId":20},"cmuzbyhvn00gc71r9tl4peyfx","Integral Tentu",[],{"id":205,"type":13,"slug":206,"title":207,"excerpt":208,"coverUrl":17,"status":18,"publishedAt":209,"featured":5,"readingMinutes":106,"order":107,"updatedAt":210,"subject":211,"levels":212,"topics":214,"tags":218,"author":17},"demo-v2-m-matematika-kuliah-1","definisi-turunan-limit","Definisi Turunan dengan Limit dan Garis Singgung","Definisi turunan dengan limit f′(x) = lim [f(x+h) − f(x)]\u002Fh, langkah menghitungnya, gradien garis singgung, syarat diferensiabel, dan contoh soal.","2026-10-08T23:58:23.002Z","2026-10-08T23:58:23.004Z",{"id":20,"slug":110,"name":111,"color":112,"icon":113},[213],{"id":169,"slug":170,"name":171},[215],{"id":216,"slug":206,"name":217,"subjectId":20},"demo-v2-topic-matematika-kuliah-1","Definisi Turunan",[],{"subjects":220,"levels":240,"topics":252,"tags":2038},[221,224,232],{"id":20,"slug":110,"name":111,"description":222,"icon":113,"color":112,"order":107,"published":5,"createdAt":223,"updatedAt":223},"Aljabar, geometri, kalkulus, statistika, dan cara berpikir matematis.","2026-10-08T09:24:40.948Z",{"id":225,"slug":226,"name":227,"description":228,"icon":229,"color":230,"order":131,"published":5,"createdAt":231,"updatedAt":231},"cmuzbyhdq000571r9nsdk6scx","fisika","Fisika","Gerak, gaya, energi, listrik, gelombang, hingga fisika modern.","atom","#0EA5E9","2026-10-08T09:24:40.958Z",{"id":233,"slug":234,"name":235,"description":236,"icon":237,"color":238,"order":136,"published":5,"createdAt":239,"updatedAt":239},"cmuzbyhdt000671r91cdnnt22","pemrograman","Pemrograman","Logika, algoritma, dan coding dari dasar sampai proyek 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Lanjut.","2026-10-08T09:24:41.498Z",{"id":350,"subjectId":20,"levelId":116,"parentId":17,"slug":1688,"name":1689,"description":1690,"order":1691,"createdAt":1692,"updatedAt":1692},"fungsi-dan-pemodelannya","Fungsi dan Pemodelannya","Fungsi dan Pemodelannya — Kelas 11 Lanjut.",18,"2026-10-08T09:24:41.504Z",{"id":386,"subjectId":225,"levelId":116,"parentId":17,"slug":1694,"name":1695,"description":1696,"order":1691,"createdAt":1697,"updatedAt":1697},"optik","Optik","Optik — Kelas 11.","2026-10-08T09:24:41.161Z",{"id":262,"subjectId":20,"levelId":116,"parentId":17,"slug":1699,"name":270,"description":1700,"order":1701,"createdAt":1702,"updatedAt":1702},"barisan-dan-deret-kelas-12-wajib","Barisan dan Deret — Kelas 12 Wajib.",19,"2026-10-08T09:24:41.512Z",{"id":559,"subjectId":225,"levelId":116,"parentId":17,"slug":1704,"name":1705,"description":1706,"order":1701,"createdAt":1707,"updatedAt":1707},"suhu-dan-kalor","Suhu dan Kalor","Suhu dan Kalor — Kelas 11.","2026-10-08T09:24:41.169Z",{"id":291,"subjectId":20,"levelId":116,"parentId":17,"slug":1709,"name":1710,"description":1711,"order":137,"createdAt":1712,"updatedAt":1712},"bunga","Bunga","Bunga — Kelas 12 Wajib.","2026-10-08T09:24:41.518Z",{"id":356,"subjectId":225,"levelId":116,"parentId":17,"slug":1714,"name":1715,"description":1716,"order":137,"createdAt":1717,"updatedAt":1717},"teori-kinetik-gas","Teori Kinetik Gas","Teori Kinetik Gas — Kelas 11.","2026-10-08T09:24:41.188Z",{"id":565,"subjectId":20,"levelId":116,"parentId":17,"slug":1719,"name":1720,"description":1721,"order":1722,"createdAt":1723,"updatedAt":1723},"investasi-dan-pinjaman","Investasi dan Pinjaman","Investasi dan Pinjaman — Kelas 12 Wajib.",21,"2026-10-08T09:24:41.525Z",{"id":583,"subjectId":225,"levelId":116,"parentId":17,"slug":1725,"name":1726,"description":1727,"order":1722,"createdAt":1728,"updatedAt":1728},"termodinamika","Termodinamika","Termodinamika — Kelas 11.","2026-10-08T09:24:41.202Z",{"id":511,"subjectId":20,"levelId":116,"parentId":17,"slug":1730,"name":1731,"description":1732,"order":1733,"createdAt":1734,"updatedAt":1734},"kaidah-pencacahan","Kaidah Pencacahan","Kaidah Pencacahan — Kelas 12 Wajib.",22,"2026-10-08T09:24:41.540Z",{"id":452,"subjectId":225,"levelId":116,"parentId":17,"slug":1736,"name":1737,"description":1738,"order":1733,"createdAt":1739,"updatedAt":1739},"listrik-statis","Listrik Statis","Listrik Statis — Kelas 12.","2026-10-08T09:24:41.215Z",{"id":422,"subjectId":225,"levelId":116,"parentId":17,"slug":1741,"name":1742,"description":1743,"order":1744,"createdAt":1745,"updatedAt":1745},"listrik-arus-searah","Listrik Arus Searah","Listrik Arus Searah — Kelas 12.",23,"2026-10-08T09:24:41.227Z",{"id":470,"subjectId":20,"levelId":116,"parentId":17,"slug":1747,"name":1597,"description":1748,"order":1744,"createdAt":1749,"updatedAt":1749},"peluang-kelas-12-wajib","Peluang — Kelas 12 Wajib.","2026-10-08T09:24:41.547Z",{"id":434,"subjectId":20,"levelId":116,"parentId":17,"slug":1751,"name":1752,"description":1753,"order":1754,"createdAt":1755,"updatedAt":1755},"geometri-analitik","Geometri Analitik","Geometri Analitik — Kelas 12 Lanjut.",24,"2026-10-08T09:24:41.553Z",{"id":428,"subjectId":225,"levelId":116,"parentId":17,"slug":1757,"name":1758,"description":1759,"order":1754,"createdAt":1760,"updatedAt":1760},"kemagnetan","Kemagnetan","Kemagnetan — Kelas 12.","2026-10-08T09:24:41.245Z",{"id":303,"subjectId":20,"levelId":116,"parentId":17,"slug":1762,"name":1763,"description":1764,"order":1765,"createdAt":1766,"updatedAt":1766},"limit","Limit","Limit — Kelas 12 Lanjut.",25,"2026-10-08T09:24:41.562Z",{"id":255,"subjectId":225,"levelId":116,"parentId":17,"slug":1768,"name":1769,"description":1770,"order":1765,"createdAt":1771,"updatedAt":1771},"listrik-ac-arus-bolak-balik","Listrik AC \u002F Arus Bolak Balik","Listrik AC \u002F Arus Bolak Balik — Kelas 12.","2026-10-08T09:24:41.263Z",{"id":493,"subjectId":225,"levelId":116,"parentId":17,"slug":1773,"name":1774,"description":1775,"order":1776,"createdAt":1777,"updatedAt":1777},"gelombang-elektromagnetik","Gelombang Elektromagnetik","Gelombang Elektromagnetik — Kelas 12.",26,"2026-10-08T09:24:41.273Z",{"id":309,"subjectId":20,"levelId":116,"parentId":17,"slug":1779,"name":1780,"description":1781,"order":1776,"createdAt":1782,"updatedAt":1782},"turunan-fungsi","Turunan Fungsi","Turunan Fungsi — Kelas 12 Lanjut.","2026-10-08T09:24:41.575Z",{"id":517,"subjectId":20,"levelId":116,"parentId":17,"slug":1784,"name":1785,"description":1786,"order":1787,"createdAt":1788,"updatedAt":1788},"aplikasi-turunan","Aplikasi Turunan","Aplikasi Turunan — Kelas 12 Lanjut.",27,"2026-10-08T09:24:41.587Z",{"id":547,"subjectId":225,"levelId":116,"parentId":17,"slug":1790,"name":1791,"description":1792,"order":1787,"createdAt":1793,"updatedAt":1793},"pengantar-instrumental-digital","Pengantar Instrumental Digital","Pengantar Instrumental Digital — Kelas 12.","2026-10-08T09:24:41.283Z",{"id":392,"subjectId":20,"levelId":116,"parentId":17,"slug":1795,"name":1796,"description":1797,"order":1798,"createdAt":1799,"updatedAt":1799},"integral","Integral","Integral — Kelas 12 Lanjut.",28,"2026-10-08T09:24:41.599Z",{"id":535,"subjectId":225,"levelId":116,"parentId":17,"slug":1801,"name":1802,"description":1803,"order":1798,"createdAt":1804,"updatedAt":1804},"relativitas-khusus","Relativitas Khusus","Relativitas Khusus — Kelas 12.","2026-10-08T09:24:41.291Z",{"id":541,"subjectId":225,"levelId":116,"parentId":17,"slug":1806,"name":1807,"description":1808,"order":1809,"createdAt":1810,"updatedAt":1810},"gejala-kuantum","Gejala Kuantum","Gejala Kuantum — Kelas 12.",29,"2026-10-08T09:24:41.303Z",{"id":440,"subjectId":20,"levelId":116,"parentId":17,"slug":1812,"name":1813,"description":1814,"order":1809,"createdAt":1815,"updatedAt":1815},"penerapan-integral","Penerapan Integral","Penerapan Integral — Kelas 12 Lanjut.","2026-10-08T09:24:41.607Z",{"id":332,"subjectId":20,"levelId":116,"parentId":17,"slug":1817,"name":1818,"description":1819,"order":1820,"createdAt":1821,"updatedAt":1821},"analisis-data-peluang","Analisis Data & Peluang","Analisis Data & Peluang — Kelas 12 Lanjut.",30,"2026-10-08T09:24:41.611Z",{"id":476,"subjectId":225,"levelId":116,"parentId":17,"slug":1823,"name":1824,"description":1825,"order":1820,"createdAt":1826,"updatedAt":1826},"fisika-inti-dan-radioaktivitas","Fisika Inti dan Radioaktivitas","Fisika Inti dan Radioaktivitas — Kelas 12.","2026-10-08T09:24:41.318Z",{"id":1828,"subjectId":20,"levelId":116,"parentId":17,"slug":1829,"name":1830,"description":1831,"order":1832,"createdAt":1833,"updatedAt":1833},"cmuzbyhw700gw71r9o87lq7vd","logaritma","Logaritma","Logaritma — Kelas 12 Lanjut.",31,"2026-10-08T09:24:41.623Z",{"id":1835,"subjectId":20,"levelId":116,"parentId":17,"slug":1836,"name":1837,"description":1838,"order":1839,"createdAt":1840,"updatedAt":1840},"cmuzbyhw900gy71r9d9sjh9ie","program-linier","Program Linier","Program Linier — Kelas 12 Lanjut.",32,"2026-10-08T09:24:41.625Z",{"id":1842,"subjectId":20,"levelId":116,"parentId":17,"slug":1843,"name":1844,"description":1845,"order":1846,"createdAt":1847,"updatedAt":1847},"cmuzbyhwb00h071r97764r7hr","bangun-ruang","Bangun Ruang","Bangun Ruang — Kelas 12 Lanjut.",33,"2026-10-08T09:24:41.627Z",{"id":216,"subjectId":20,"levelId":169,"parentId":17,"slug":206,"name":217,"description":208,"order":1849,"createdAt":1850,"updatedAt":1850},100,"2026-10-08T23:58:22.977Z",{"id":121,"subjectId":20,"levelId":116,"parentId":17,"slug":14,"name":122,"description":16,"order":1849,"createdAt":1852,"updatedAt":1852},"2026-10-08T23:58:22.868Z",{"id":1854,"subjectId":233,"levelId":116,"parentId":17,"slug":1855,"name":1856,"description":1857,"order":1849,"createdAt":1858,"updatedAt":1858},"demo-v2-topic-pemrograman-sma-1","fungsi-python-def-return","Fungsi Python","Pelajari cara membuat fungsi Python dengan def, parameter, nilai default, dan return, plus perbedaan return dan print lewat contoh program yang jelas.","2026-10-08T23:58:23.661Z",{"id":1860,"subjectId":225,"levelId":164,"parentId":17,"slug":1861,"name":1862,"description":1863,"order":1849,"createdAt":1864,"updatedAt":1864},"demo-v2-topic-fisika-smp-1","glb-dan-glbb","GLB dan GLBB","Rumus GLB dan GLBB lengkap: jarak, kecepatan, percepatan, grafik posisi–waktu, perbedaan GLB dan GLBB, plus contoh soal gerak lurus dan pembahasannya.","2026-10-08T23:58:23.189Z",{"id":1866,"subjectId":225,"levelId":169,"parentId":17,"slug":1867,"name":1868,"description":1869,"order":1849,"createdAt":1870,"updatedAt":1870},"demo-v2-topic-fisika-kuliah-1","gerak-harmonik-sederhana","Gerak Harmonik Sederhana","Gerak harmonik sederhana untuk fisika dasar: persamaan x = A cos(ωt + φ), kecepatan, percepatan, periode pegas dan bandul, energi, serta contoh soal.","2026-10-08T23:58:23.364Z",{"id":1872,"subjectId":225,"levelId":116,"parentId":17,"slug":1873,"name":1874,"description":1875,"order":1849,"createdAt":1876,"updatedAt":1876},"demo-v2-topic-fisika-sma-1","hukum-newton-2","Hukum Newton 2","Hukum Newton 2: bunyi, rumus ΣF = m·a, diagram gaya, gaya gesek statis dan kinetis, serta contoh soal mencari percepatan dan massa beserta pembahasan.","2026-10-08T23:58:23.280Z",{"id":1878,"subjectId":233,"levelId":169,"parentId":17,"slug":1879,"name":1880,"description":1881,"order":1849,"createdAt":1882,"updatedAt":1882},"demo-v2-topic-pemrograman-kuliah-1","notasi-big-o-kompleksitas-waktu","Notasi Big O","Pahami notasi Big O dan kompleksitas waktu algoritma: O(1), O(log n), O(n), O(n²), cara menghitungnya dari kode Python, dan contoh soalnya.","2026-10-08T23:58:23.797Z",{"id":1884,"subjectId":233,"levelId":160,"parentId":17,"slug":1885,"name":1886,"description":1887,"order":1849,"createdAt":1888,"updatedAt":1888},"demo-v2-topic-pemrograman-sd-1","pengertian-algoritma","Pengertian Algoritma","Algoritma adalah langkah-langkah urut untuk menyelesaikan masalah. Pelajari pengertian, ciri, dan contoh algoritma sehari-hari untuk siswa SD.","2026-10-08T23:58:23.477Z",{"id":1890,"subjectId":225,"levelId":160,"parentId":17,"slug":1891,"name":1892,"description":1893,"order":1849,"createdAt":1894,"updatedAt":1894},"demo-v2-topic-fisika-sd-1","pengukuran-panjang","Pengukuran Panjang","Belajar pengukuran panjang untuk SD: satuan baku, alat ukur panjang, cara memakai penggaris, dan tangga satuan panjang km sampai mm + contoh soal.","2026-10-08T23:58:23.095Z",{"id":1896,"subjectId":20,"levelId":160,"parentId":17,"slug":1897,"name":1898,"description":1899,"order":1849,"createdAt":1900,"updatedAt":1900},"demo-v2-topic-matematika-sd-1","penjumlahan-pecahan","Penjumlahan Pecahan","Cara penjumlahan pecahan berpenyebut sama dan beda penyebut memakai KPK, pecahan senilai, dan pecahan campuran, lengkap dengan contoh soal SD.","2026-10-08T23:58:22.508Z",{"id":1902,"subjectId":20,"levelId":164,"parentId":17,"slug":1903,"name":1904,"description":1905,"order":1849,"createdAt":1906,"updatedAt":1906},"demo-v2-topic-matematika-smp-1","teorema-pythagoras","Teorema Pythagoras","Teorema Pythagoras a² + b² = c² untuk mencari sisi miring dan sisi siku-siku, tripel Pythagoras, diagonal ruang balok, dan contoh soal kelas 8.","2026-10-08T23:58:22.690Z",{"id":1908,"subjectId":233,"levelId":164,"parentId":17,"slug":1909,"name":1910,"description":1911,"order":1849,"createdAt":1912,"updatedAt":1912},"demo-v2-topic-pemrograman-smp-1","variabel-dan-tipe-data-python","Variabel dan Tipe Data Python","Belajar variabel dan tipe data Python dari nol: int, float, string, boolean, operator, print, dan input, lengkap dengan contoh program dan latihan.","2026-10-08T23:58:23.562Z",{"id":1914,"subjectId":233,"levelId":169,"parentId":17,"slug":1915,"name":1916,"description":1917,"order":1918,"createdAt":1919,"updatedAt":1919},"demo-v2-topic-pemrograman-kuliah-2","class-dan-object-python","Class dan Object Python","Pelajari class dan object Python untuk OOP: __init__, self, atribut, method, inheritance, dan invarian objek lewat contoh program dompet digital.",101,"2026-10-08T23:58:23.830Z",{"id":1921,"subjectId":20,"levelId":116,"parentId":17,"slug":1922,"name":1923,"description":1924,"order":1918,"createdAt":1925,"updatedAt":1925},"demo-v2-topic-matematika-sma-2","eksponen-dan-logaritma","Eksponen dan Logaritma","Materi eksponen dan logaritma kelas 10: sifat-sifat eksponen, definisi dan sifat logaritma, persamaan eksponen dan logaritma, serta contoh soal.","2026-10-08T23:58:22.902Z",{"id":1927,"subjectId":225,"levelId":160,"parentId":17,"slug":1928,"name":1929,"description":1930,"order":1918,"createdAt":1931,"updatedAt":1931},"demo-v2-topic-fisika-sd-2","macam-macam-gaya","Gaya dan Macam-Macamnya","Gaya adalah tarikan atau dorongan. Pelajari macam-macam gaya (otot, gravitasi, magnet, gesek, pegas), pengaruhnya pada benda, dan contoh soalnya.","2026-10-08T23:58:23.126Z",{"id":1933,"subjectId":20,"levelId":160,"parentId":17,"slug":1934,"name":1935,"description":1936,"order":1918,"createdAt":1937,"updatedAt":1937},"demo-v2-topic-matematika-sd-2","rumus-keliling-dan-luas-bangun-datar","Keliling dan Luas Bangun Datar","Rumus keliling dan luas bangun datar: persegi, persegi panjang, segitiga, jajargenjang, trapesium, dan lingkaran, dengan cara mudah dan contoh soal.","2026-10-08T23:58:22.588Z",{"id":1939,"subjectId":233,"levelId":116,"parentId":17,"slug":1940,"name":1941,"description":1942,"order":1918,"createdAt":1943,"updatedAt":1943},"demo-v2-topic-pemrograman-sma-2","list-dan-dictionary-python","List dan Dictionary Python","Pahami list dan dictionary Python: indeks, append, key-value, get, dan perulangan, plus perbedaan keduanya lewat contoh pengolahan data nilai siswa.","2026-10-08T23:58:23.694Z",{"id":1945,"subjectId":225,"levelId":164,"parentId":17,"slug":1946,"name":1947,"description":1948,"order":1918,"createdAt":1949,"updatedAt":1949},"demo-v2-topic-fisika-smp-2","rumus-massa-jenis","Massa Jenis","Rumus massa jenis ρ = m\u002FV lengkap dengan satuan kg\u002Fm³ dan g\u002Fcm³, tabel massa jenis air, besi, dan minyak, cara menghitung, serta contoh soal pembahasan.","2026-10-08T23:58:23.217Z",{"id":1951,"subjectId":233,"levelId":164,"parentId":17,"slug":1952,"name":1953,"description":1954,"order":1918,"createdAt":1955,"updatedAt":1955},"demo-v2-topic-pemrograman-smp-2","percabangan-python-if-else","Percabangan Python","Pelajari percabangan Python dengan if, elif, dan else: operator perbandingan, operator logika, dan contoh program nilai rapor lengkap dengan outputnya.","2026-10-08T23:58:23.592Z",{"id":1957,"subjectId":233,"levelId":160,"parentId":17,"slug":1958,"name":1959,"description":1960,"order":1918,"createdAt":1961,"updatedAt":1961},"demo-v2-topic-pemrograman-sd-2","percabangan-dalam-algoritma","Percabangan dalam Algoritma","Percabangan dalam algoritma memilih tindakan berdasarkan syarat jika-maka. Pelajari pengertian, contoh sehari-hari, dan simbol flowchart-nya.","2026-10-08T23:58:23.503Z",{"id":1963,"subjectId":20,"levelId":164,"parentId":17,"slug":1964,"name":1965,"description":1966,"order":1918,"createdAt":1967,"updatedAt":1967},"demo-v2-topic-matematika-smp-2","persamaan-garis-lurus","Persamaan Garis Lurus","Persamaan garis lurus y = mx + c, rumus gradien dari dua titik, garis sejajar dan tegak lurus, cara menggambar grafik, serta contoh soal kelas 8.","2026-10-08T23:58:22.730Z",{"id":1969,"subjectId":225,"levelId":169,"parentId":17,"slug":1970,"name":1971,"description":1972,"order":1918,"createdAt":1973,"updatedAt":1973},"demo-v2-topic-fisika-kuliah-2","usaha-oleh-gaya-berubah","Usaha Gaya Berubah","Usaha oleh gaya berubah dengan integral W = ∫F dx, rumus usaha W = F·s sebagai dot product, usaha pegas, dan teorema usaha–energi, plus contoh soal.","2026-10-08T23:58:23.394Z",{"id":1975,"subjectId":20,"levelId":116,"parentId":17,"slug":1976,"name":1977,"description":1978,"order":1979,"createdAt":1980,"updatedAt":1980},"demo-v2-topic-matematika-sma-3","rumus-peluang","Peluang Kejadian","Rumus peluang P(A) = n(A)\u002Fn(S), ruang sampel, peluang komplemen, frekuensi harapan, kejadian saling lepas dan saling bebas, plus contoh soal dadu dan koin.",102,"2026-10-08T23:58:22.934Z",{"id":1982,"subjectId":233,"levelId":116,"parentId":17,"slug":1983,"name":1984,"description":1985,"order":1979,"createdAt":1986,"updatedAt":1986},"demo-v2-topic-pemrograman-sma-3","pencarian-linear-dan-biner","Pencarian Linear dan Biner","Pelajari pencarian linear dan pencarian biner (binary search): cara kerja, syarat data terurut, kode Python, dan perbandingan jumlah langkahnya.","2026-10-08T23:58:23.724Z",{"id":1988,"subjectId":233,"levelId":164,"parentId":17,"slug":1989,"name":1990,"description":1991,"order":1979,"createdAt":1992,"updatedAt":1992},"demo-v2-topic-pemrograman-smp-3","perulangan-python-for-while","Perulangan Python","Pelajari perulangan Python dengan for, range(), dan while, lengkap dengan contoh program menghitung total, break, continue, dan latihan soal.","2026-10-08T23:58:23.624Z",{"id":1994,"subjectId":233,"levelId":160,"parentId":17,"slug":1995,"name":1996,"description":1997,"order":1979,"createdAt":1998,"updatedAt":1998},"demo-v2-topic-pemrograman-sd-3","perulangan-dalam-algoritma","Perulangan dalam Algoritma","Perulangan dalam algoritma mengulang langkah yang sama beberapa kali. Pelajari pengertian, contoh perulangan sehari-hari, dan cara menghitung hasilnya.","2026-10-08T23:58:23.529Z",{"id":2000,"subjectId":20,"levelId":164,"parentId":17,"slug":2001,"name":2002,"description":2003,"order":1979,"createdAt":2004,"updatedAt":2004},"demo-v2-topic-matematika-smp-3","rumus-prisma-dan-limas","Prisma dan Limas","Rumus volume prisma dan limas, luas permukaan, sifat sisi-rusuk-titik sudut, jaring-jaring, limas 3D interaktif, dan contoh soal bangun ruang sisi datar.","2026-10-08T23:58:22.780Z",{"id":2006,"subjectId":233,"levelId":169,"parentId":17,"slug":2007,"name":2008,"description":2009,"order":1979,"createdAt":2010,"updatedAt":2010},"demo-v2-topic-pemrograman-kuliah-3","unit-test-python","Unit Test Python","Pelajari unit test Python dengan modul unittest: assertEqual, assertRaises, nilai batas, dan cara menjalankan tes, lengkap dengan contoh dan versi pytest.","2026-10-08T23:58:23.864Z",{"id":186,"subjectId":20,"levelId":169,"parentId":17,"slug":176,"name":187,"description":178,"order":1979,"createdAt":2012,"updatedAt":2012},"2026-10-08T23:58:23.045Z",{"id":2014,"subjectId":20,"levelId":160,"parentId":17,"slug":2015,"name":2016,"description":2017,"order":1979,"createdAt":2018,"updatedAt":2018},"demo-v2-topic-matematika-sd-3","rumus-volume-kubus","Volume dan Luas Permukaan Kubus","Rumus volume kubus V = s³ dan luas permukaan kubus L = 6s², sifat kubus, jaring-jaring, kubus 3D interaktif, dan contoh soal bertingkat.","2026-10-08T23:58:22.619Z",{"id":2020,"subjectId":20,"levelId":164,"parentId":17,"slug":2021,"name":2022,"description":2023,"order":2024,"createdAt":2025,"updatedAt":2025},"demo-v2-topic-matematika-smp-4","rumus-tabung-dan-kerucut","Tabung dan Kerucut","Rumus volume tabung dan kerucut, luas permukaan, garis pelukis, jaring-jaring berupa persegi panjang dan juring, kerucut 3D interaktif, dan contoh soal.",103,"2026-10-08T23:58:22.828Z",{"id":2027,"subjectId":233,"levelId":116,"parentId":17,"slug":2028,"name":2029,"description":2030,"order":2024,"createdAt":2031,"updatedAt":2031},"demo-v2-topic-pemrograman-sma-4","try-except-python","Try Except dan Membaca File","Pelajari try except Python untuk menangani error seperti ValueError dan FileNotFoundError, serta cara membaca dan menulis file txt dengan with open.","2026-10-08T23:58:23.755Z",{"id":2033,"subjectId":20,"levelId":160,"parentId":17,"slug":2034,"name":2035,"description":2036,"order":2024,"createdAt":2037,"updatedAt":2037},"demo-v2-topic-matematika-sd-4","rumus-volume-balok","Volume dan Luas Permukaan Balok","Rumus volume balok V = p × l × t dan luas permukaan balok L = 2(pl + pt + lt), sifat balok, jaring-jaring, balok 3D interaktif, dan contoh soal.","2026-10-08T23:58:22.651Z",[]]