Quadratic Function Plotter (ax² + bx + c)
Plot any quadratic function ax² + bx + c. Get the vertex, discriminant, real roots and a smooth parabola chart. Instant, free.
How to use this tool
- Enter coefficient a (x²), coefficient b (x), constant c, x minimum and x maximum in the fields above.
- Results update instantly as you type — or click Calculate.
- Read your vertex x and the full breakdown beneath it.
A quadratic function f(x) = ax² + bx + c forms a parabola. The vertex is at x = −b/(2a). Real roots exist when the discriminant b²−4ac ≥ 0; they are x = (−b ± √(b²−4ac)) / 2a.
Frequently asked questions
- What does the discriminant tell me?
- If b²−4ac > 0 there are two real roots; = 0 one repeated root; < 0 no real roots (the parabola doesn't cross the x-axis).
- Does a affect the shape?
- Yes. a > 0 opens upward; a < 0 opens downward. Larger |a| makes it narrower.