Parabola Vertex Finder

A parabola is a curve that results from plotting a quadratic equation on the x-y plane. It shows how the value of "y" (vertical movement) corresponds to a certain value of x when plugged into the quadratic equation.

Any quadratic equation is in the form of ax²+bx+c and when a is less than 0 (i.e. negative) you get a parabola that opens downwards, this is because no matter how large the value of x, the negative sign in front of x² results in a negative number almost every time. The only instances where it will result in a non-negative number is when bx and c together "cancel out" or are greater than -ax².

The part where the parabola makes a "U-turn" is called the vertex. This is either the maximum or the minimum value of y. This means the vertical movement of this point is 'capped' by the equation. And conversely, when a is positive you have a parabola that opens upward.

In fact you can see below in the appendix section, the precise point at which the bx and c terms "cancel out" the ax² term resulting in a zero. This value of x can also be worked out by factorising the equation, or through the quadratic formula.

This calculator shows you both the "brute forced" vertex - it generates a table of 1000 possible values of x greater and lesser than the one you enter, and shows you exactly at what value of x it was that y hit the vertex; but since this is iterative the answer is often less than precise. The vertex is best found mathematically using -b/2a and we compare the difference.