Parabola Properties
Enter the coefficients of a parabola y = ax² + bx + c. The calculator returns the vertex (h, k), the axis of symmetry, the direction it opens, the focus and the directrix, plus the y-intercept and any x-intercepts.
Frequently asked questions
How is the vertex found?
By completing the square: h = −b/(2a) and k = c − b²/(4a).
What is the focus of a parabola?
A point on the axis of symmetry such that every point on the parabola is equidistant from the focus and the directrix. For y = ax² + bx + c it sits at (h, k + 1/(4a)).
Which way does the parabola open?
Upward when a > 0, downward when a < 0. The sign of the leading coefficient controls the direction.