Quadratic Function Explorer
Drag a, b and c to see the parabola, roots, vertex and discriminant change.
Equationy = x²
Vertex–
Axis of symmetry–
Discriminant–
Roots (x-intercepts)–
y-intercept–
What you can learn
- a controls the opening direction and width; c is the y-intercept.
- The vertex is at x = -b / 2a and the axis of symmetry passes through it.
- The discriminant b² - 4ac tells you if there are two, one or no real roots.
Frequently asked questions
What does the discriminant tell me?
If b² - 4ac is positive there are two real roots, if zero there is one repeated root, and if negative there are no real roots (the parabola misses the x-axis).
How do I find the vertex of a parabola?
The x-coordinate is -b / 2a. Substitute it back into the equation to get the y-coordinate.