Quadratic Equation Visualizer

Interactive tool to graph parabolas and solve quadratic equations instantly.

Master the Quadratic Equation by seeing how the numbers (coefficients) change the shape of the graph. Stop memorizing formulas and start visualizing the math.

✓ Interactive Graph✓ Real-Time Roots✓ Vertex Calculation✓ Free for Students

Equation Coefficients

1x² + 0x + 0 = 0

a (Quadratic Term)1

-10010

b (Linear Term)0

-10010

c (Constant Term)0

-20020

Interactive Graph

Solution & Properties

Discriminant (Δ)

0.00

One Real Root

Vertex

(0.00, 0.00)

Turning Point

Roots (x-intercepts):

x = 0.000

Step-by-Step Solution

Step 1: Identify Coefficients

For the standard quadratic equation $ax^2 + bx + c = 0$ :

a = 1

b = 0

c = 0

Step 2: Calculate Discriminant ( $\Delta$ )

The discriminant tells us the nature of the roots:

\Delta = b^2 - 4ac

\Delta = (0)^2 - 4(1)(0)

\Delta = 0 - (0)

\Delta = 0

Since $\Delta = 0$ , we have one repeated real root.

Step 3: Quadratic Formula

Substitute values into the formula:

x = \frac{-b \pm \sqrt{\Delta}}{2a}

x = \frac{-(0) \pm \sqrt{0}}{2(1)}

x = \frac{0 \pm 0.00}{2}

Step 4: Solve for x

Repeated Root

x = \frac{0}{2}

$x = 0.000$

What is Quadratic Equation Visualizer?

What is a Quadratic Equation?

A quadratic equation is a polynomial equation of degree 2. It forms a curve called a Parabola. The standard form is:

ax² + bx + c = 0

Where x is the unknown variable, and a, b, c are constants.

a (Quadratic Term): Controls the width and direction. If a > 0, it opens UP (smiley). If a < 0, it opens DOWN (frown).
b (Linear Term): Shifts the parabola left or right (and up/down).
c (Constant Term): The vertical offset. This is where the graph passes through the Y-axis (y-intercept).

Formula & Calculation

To find the "roots" (where the graph touches the X-axis), we use the famous Quadratic Formula:

x = -b ± √(b² - 4ac)2a

The Discriminant (Δ)

The part inside the square root, b² - 4ac, tells us about the roots:

Positive (>0): Two distinct real roots.
Zero (=0): One real root (vertex touches X-axis).
Negative (<0): No real roots (complex numbers).Graph floats above/below axis.

Example Calculation

Projectile Motion Example

Imagine throwing a ball into the air. Its height h at time t is modeled by:

h(t) = -5t² + 20t + 2

a = -5: Gravity pulling it down (parabola opens down).
b = 20: Initial upward velocity.
c = 2: Initial height (2 meters off ground).

Using the visualizer, you can see the maximum height (vertex) and when it hits the ground (root).

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Frequently Asked Questions

Why do we learn this?

Recursion, orbits, business profit optimization, and physics engines in video games all rely on quadratic relationships.

What if 'a' is zero?

Then it's not a quadratic equation anymore! It becomes a linear equation (bx + c = 0), which is just a straight line.