Associated Topics || Dr. Math Home || Search Dr. Math

### Vertex of a Parabola

```Date: 04/16/2002 at 22:05:40
From: Chris
Subject: Vertex of a Parabola

What is the quickest annd easiest way to find the y-coordinate of the
vertex? I know that the x-coordinate is -b/2a. Is the best way to plug
that value into the equation y = ax^2+bx+c, or is there a special
formula that will get the answer quicker?
```

```
Date: 04/17/2002 at 07:48:25
From: Doctor Floor
Subject: Re: Vertex of a Parabola

Hi, Chris,

Of course we can MAKE the formula by plugging in the x-coordinate:

y = a(-b/2a)^2 + b*(-b/2a) + c

a*b^2   b^2
= ----- - --- + c
4a^2    2a

b^2   b^2
=  --- - --- + c
4a    2a

b^2
= c - ---
4a

Completing the Square
http://www.mathforum.org/library/drmath/view/53102.html

Here the vertex is derived by completing the square, and is found
from the formula given in step 5.

If you have more questions, just write back.

Best regards,
- Doctor Floor, The Math Forum
http://mathforum.org/dr.math/
```
Associated Topics:
High School Basic Algebra
High School Coordinate Plane Geometry

Search the Dr. Math Library:

 Find items containing (put spaces between keywords):   Click only once for faster results: [ Choose "whole words" when searching for a word like age.] all keywords, in any order at least one, that exact phrase parts of words whole words

Submit your own question to Dr. Math
Math Forum Home || Math Library || Quick Reference || Math Forum Search