Quadratic Function Visualizer

Visualize and analyze quadratic functions interactively

📊 Properties

Equation
y = x²
Vertex
(0.00, 0.00)
Axis of Symmetry
x = 0.00
Y-Intercept
(0, 0)
Direction
Opens Upward ⬆️

🔍 Roots Analysis

Discriminant
Δ = 0.00
One real root
X-Intercepts (Roots)
x = 0.00

Try These Examples

📈Formula

y = ax² + bx + c

💡How it works

Quadratic functions form parabolas. The coefficient 'a' determines the direction and width, 'b' affects the horizontal position, and 'c' is the y-intercept.

ℹ️ What is Visual Quadratic Solver?

A visual quadratic solver shows the parabola of ax² + bx + c = 0 alongside the algebraic solution, making it easier to understand how the equation's roots correspond to where the parabola crosses the x-axis. It bridges the gap between algebraic manipulation and geometric intuition.

📐 Formula

y = ax² + bx + c | Vertex: (−b/2a, c − b²/4a)
a— Coefficient of x² — determines parabola opening direction and width
b— Coefficient of x — determines horizontal position of vertex
c— Constant term — y-intercept of the parabola
Vertex— Minimum (a>0) or maximum (a<0) point of the parabola

✏️ Worked Example

a: 1
b: -2
c: -3
  1. 1Vertex x = −(−2)/(2×1) = 1
  2. 2Vertex y = 1² − 2(1) − 3 = −4 → vertex at (1, −4)
  3. 3Discriminant = (−2)² − 4(1)(−3) = 4 + 12 = 16
  4. 4Roots = (2 ± 4) / 2 → x = 3 or x = −1
  5. 5y-intercept: set x=0 → y = −3
✅ Result: Parabola opens up, vertex (1,−4), roots at x=3 and x=−1

💡 How to Interpret Results

  • ▸If a > 0: parabola opens UP (U-shape) — vertex is a minimum.
  • ▸If a < 0: parabola opens DOWN (∩-shape) — vertex is a maximum.
  • ▸The roots are symmetric about the vertex x-coordinate (axis of symmetry).
  • ▸The vertex y-value is the minimum or maximum value of the quadratic.
  • ▸Changing c shifts the parabola vertically; changing b shifts the vertex horizontally.

❓ Frequently Asked Questions

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