Solving Quadratic Equations with the Quadratic Formula

Overview

A whiteboard‑style animation that introduces quadratic equations, explains the quadratic formula and discriminant, and walks through a concrete example $x^{2}+5x+6=0$. The goal is for SSC‑level students to see each algebraic step highlighted in colour and understand how the discriminant determines the nature of the roots.

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Phases

#	Phase Name	Duration	Description
1	Intro	~5s	Hand‑drawn title appears: “Quadratic Equation – Solution by Formula”. A simple sketch of a parabola and the generic form $ax^{2}+bx+c=0$ is written.
2	Formula Introduction	~12s	The quadratic formula $x = \frac{-b \pm \sqrt{b^{2}-4ac}}{2a}$ is written in bold colour. Each component (‑b, ±, √, denominator) is highlighted sequentially as the narrator explains its role.
3	Discriminant Explanation	~15s	The discriminant $D = b^{2}-4ac$ is isolated, coloured, and three cases are illustrated with small sketches: $D>0$ (two distinct real roots), $D=0$ (one repeated real root), $D<0$ (complex roots). Brief visual cue (green, orange, red) accompanies each case.
4	Example Setup	~8s	The equation $x^{2}+5x+6=0$ is written. Coefficients $a=1, b=5, c=6$ are boxed.
5	Compute Discriminant	~10s	Substituting into $D = b^{2}-4ac$: steps shown one‑by‑one, numbers appear, colour‑highlight the subtraction result $D=25-24=1$.
6	Apply Formula – Numerator	~12s	Numerator $-b \pm \sqrt{D}$ is built stepwise: first $-b = -5$, then $\sqrt{D}=1$, then the two possibilities $-5+1$ and $-5-1$. Each intermediate expression is highlighted.
7	Final Roots	~10s	Division by $2a = 2$ is performed, yielding $x = -2$ and $x = -3$. The two roots appear side‑by‑side, each with a green check mark.
8	Summary & Outro	~8s	Recap bullet points (formula, discriminant meaning, example result) appear briefly. Fade‑out with “Practice more!” in Bengali.

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Layout

┌─────────────────────────────────────────────┐
│                 TOP AREA                    │
├───────────────────────┬─────────────────────┤
│                       │                     │
│      LEFT AREA        │      RIGHT AREA     │
│  (main whiteboard)    │ (small notes/      │
│                       │  case icons)        │
├───────────────────────┴─────────────────────┤
│                 BOTTOM AREA                │
└─────────────────────────────────────────────┘

Area Descriptions

Area	Content	Notes
Top	Title of the segment (e.g., “Quadratic Formula”)	Fades in at the start of each major phase
Left	Hand‑drawn whiteboard content: equations, substitutions, algebraic manipulations	Primary focus; colour highlights follow the narration
Right	Small icons illustrating discriminant cases (green‑check, orange‑dash, red‑cross) and brief Bengali keywords ("বাস্তব", "সমান", "জটিল")	Remains visible after Phase 3 for reference
Bottom	Final summary bullets in Bengali, and a tiny citation “SSC Mathematics”	Appears in the final phase only

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Notes

• All handwriting‑style strokes should be smooth and slightly delayed to mimic a teacher drawing on a board.
• Colour palette: dark blue for base text, orange for highlighted parts of the formula, green for correct/real‑root indicators, red for complex‑root warning.
• No spoken text is required in the spec, but the visual timing assumes a friendly Bengali narration that matches the highlighted steps.
• The entire scene fits within a single Manim Scene class.
• Total runtime ≈ 80 seconds, well within the 1–2 minute target.