How can you use the quadratic formula to find the vertex of a parabola?

1 Answer
Bill K.
Nov 3, 2015

Average the roots that come from the quadratic formula to see that the x-coordinate of the vertex of ax^2+bx+c=0 is x=-b/(2a).

Explanation:

The quadratic formula says the roots of the quadratic equation ax^2+bx+c=0 are x=(-b pm sqrt(b^2-4ac))/(2a).

Whether these roots are real or complex numbers, when you average the two, the square roots cancel and you get x=((-2b)/(2a))/2=-b/(2a).

This clearly gives the vertex when there are x-intercepts (since the vertex is (horizontally) halfway between the intercepts). It also happens to work when the roots are complex numbers.

Related questions
See all questions in Quadratic Formula
Impact of this question
3085 views around the world
You can reuse this answer
Creative Commons License