The Quadratic Parabola

Description

This animation explores the standard form of a quadratic y = ax² + bx + c by animating each coefficient. Students see how 'a' controls width and direction, 'c' shifts the parabola vertically, and the vertex traces a path as parameters change. The formula updates in real time alongside the graph.

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Phases

#	Phase Name	Duration	Description
1	Introduction	5s	Draw axes, display formula, plot initial parabola (a=1, b=0, c=0)
2	Coefficient a	15s	Animate a from 1 → 3 (narrow), 3 → -2 (flip), -2 → 1 (restore); vertex dot tracks
3	Coefficient c	12s	Animate c from 0 → 3 (up), 3 → -3 (down), -3 → 0 (restore)
4	Summary	8s	Show all labeled parts; highlight vertex formula; fade out

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Layout

+-----------------------------------------------+
|  y = ax² + bx + c           [formula top-left]|
|  a = 1.00  b = 0.00  c = 0.00                 |
|                                                |
|        ^                                       |
|        |      * <- vertex dot                  |
|        |     / \                               |
|  ------+----/---\-------->                     |
|        |   /     \                             |
|                                                |
+-----------------------------------------------+

Area Descriptions

Area	Content	Notes
Center	Axes + parabola curve	always_redraw based on ValueTrackers
Top left	MathTex formula	Color-coded: a=RED, b=GREEN, c=BLUE
Below formula	Decimal value readouts	a, b, c current values
On graph	Vertex dot (orange)	Tracks vertex at (-b/2a, f(-b/2a))

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Assets & Dependencies

• Fonts: LaTeX
• Colors: PARABOLA_COLOR = YELLOW, VERTEX_COLOR = ORANGE, a=RED, b=GREEN, c=BLUE, BG = #1a1a2e
• Manim version: ManimCE 0.19.1

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Notes

• Keep b=0 throughout most of animation to keep vertex on y-axis and vertex formula simple
• Vertex x = -b/(2a), guard against a=0
• Axes range: x: [-4, 4], y: [-5, 7]