Solving x^2-5x+6=0 by Factoring
This animation walks through solving a quadratic equation by splitting the middle term, factoring into two binomials, and connecting the solution to a graph. It shows how -5x becomes -2x and -3x based on numbers that multiply to 6 and add to -5, then reveals how x=2 and x=3 correspond to where the parabola y=x^2-5x+6 crosses the x-axis. Useful for students learning to link algebraic factoring with graphical roots.
Narrated · 16:9 · every frame verified for overlaps, spacing and edges before rendering
The prompt that made it
Scene 1: The Problem (0:00 - 0:10) Visual: A clean, empty grid appears (like graph paper). Action: The equation x 2 − 5 x + 6 = 0 x 2 −5x+6=0 floats in the center of the screen in white text. Audio: Whoosh sound. Narrator: "Let’s solve this quadratic equation visually." Scene 2: The Splitting of the Middle Term (0:10 - 0:25) Visual: The equation morphs. The "-5x" splits into two glowing segments: "-2x" and "-3x". Action: The screen shows: x 2 − 2 x − 3 x + 6 = 0 x 2 −2x−3x+6=0. Highlight: The "-2" and "-3" pulse in Yellow to show they add up to -5 and multiply to 6. Audio: Soft chime as the numbers find their pair. Scene 3: Factoring (0:25 - 0:45) Visual: The equation reorganizes itself into two parenthesis groups. Action: ( x − 2 ) ( x − 3 ) = 0 (x−2)(x−3)=0 slides into place. The parentheses look like physical brackets (3D blocks) locking the terms inside. Visual Effect: The two brackets separate to the left and right sides of the screen. Scene 4: The Graph Emerges (0:45 - 1:10) Visual: A 3D Cartesian plane (X and Y axes) rises up from the bottom of the screen. Action: A bright Cyan curve (The Parabola) draws itself smoothly across the screen. It dips down at the bottom. Highlight: The curve is clearly the visual representation of y = x 2 − 5 x + 6 y=x 2 −5x+6. Scene 5: The Roots (The "Sum" Answer) (1:10 - 1:30) Visual: The camera zooms in on where the Cyan curve touches the X-axis. Action: First Root: At point x = 2 x=2, a bright Orange Dot explodes onto the intersection. Text appears: x = 2 x=2. Second Root: At point x = 3 x=3, another Orange Dot appears. Text appears: x = 3 x=3. Highlight: The curve glows brighter as if "satisfied" that it has found its anchors. Scene 6: The Verification (1:30 - 1:45) Visual: A "Check Mark" (✓) draws itself over the graph. Action: The screen splits. On the left, we see the algebraic steps ( x = 2 , x = 3 x=2,x=3). On the right, we see the graph intersections. Animation: Lines draw a connection from the algebra to the graph, proving they match perfectly. Scene 7: The Summary (1:45 - 2:00) Visual: The equation, the graph, and the roots ( x = 2 x=2 and x = 3 x=3) float together. Action: The text "The Parabola meets the world where Y equals zero" fades in. Audio: Soft orchestral hit. Narrator: "And that’s how you solve a sum graphically."
Make the next one in this series
- Show how the quadratic formula gives the same roots x=2 and x=3.
- Animate completing the square for x^2-5x+6=0 step by step.
- Compare factoring when the discriminant is negative and roots are complex.
