# How do I convert the equation #f(x)=x^2-8x+15# to vertex form?

##### 2 Answers

To convert this equation into vertex form, you want to use a method called completing the square. I will walk you through the steps to do this:

First, group the first two terms together in brackets for now, and common factor the coefficient beside

#f(x)=(x^2−8x)+15#

Next, take the x term (-8x), divide it by 2x, square it, then add and subtract that number inside the brackets so as to not change the meaning of the equation (16-16=0, therefore no change) like so:

#((−8x)/(2x))^2=16#

#f(x)=(x^2−8x+16−16)+15#

Now, take the subtracted term (-16) and multiply it by the coefficient outside of the brackets (there is none so skip this), and move it outside of the brackets:

#f(x)=(x^2−8x+16)+15−16#

Now, simplify the outside of the brackets, then change the

#(-8x)/(2x) = -4#

#f(x)=(x−4)^2−1#

And that's it! The original equation is now in vertex form! In case you were wondering or didn't know, the vertex

Hopefully I was of some help and hopefully you've understood this! :)

The vertex form is

or, by expansion:

The only term with

Therefore,

Substituting

We have

For this to be equivalent to the standard form:

With