How do you find the vertex of a parabola?

Answer 1

Solution 1Start by putting the parabola's equation into the form

y = ax2 + bx + c if it opens up or down,

or x = ay2 + by + c if it is opens to the left or right,

where a, b, and c are constants.

The x-value for the vertex is -(b/2a). You can use this x-value to solve for the y-value by substituting the x value in the original quadratic equation.

Solution 2Put the parabola's equation into this form:

y - k = 4p(x - h)2

or x - h = 4p(y - k)2

You just need to simplify the equation until it looks like this. The vertex is located at the coordinates (h,k). (p is for the focus, but that isn't important as long as you know h and k.)