Quadratic Graph Simulator

Adjust a, b, and c to simulate a parabola and its key features

Quadratic Formulas

Standard form	y = ax^2 + bx + c
Vertex x-coordinate	x = -b / 2a
Axis of symmetry	x = -b / 2a
Discriminant	D = b^2 - 4ac

Step-by-Step Example

For y = x^2 - 2x - 3, the vertex x-value is -(-2)/(2 x 1) = 1. Substituting x = 1 gives y = -4, so the vertex is (1, -4). The discriminant is 16, so the graph has two real x-intercepts.

Practical Rules

If a is positive, the parabola opens upward.
If a is negative, the parabola opens downward.
If the discriminant is positive, the graph crosses the x-axis twice.
If the discriminant is zero, the graph touches the x-axis at the vertex.

Frequently Asked Questions

What is a quadratic graph?▼

A quadratic graph is the graph of y = ax^2 + bx + c. Its shape is a parabola that opens upward when a is positive and downward when a is negative.

How do you find the vertex of a quadratic?▼

The vertex x-coordinate is -b divided by 2a. Substitute that x-value into the quadratic equation to find the y-coordinate.

What does coefficient a do?▼

The coefficient a controls the opening direction and width of the parabola. Larger absolute values make it narrower.

What is the axis of symmetry?▼

The axis of symmetry is the vertical line x = -b/(2a) that passes through the vertex.

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