# What is the vertex form of #y= x^2 -6x+8 #?

##### 1 Answer

#### Explanation:

The general vertex form is

To convert

For a squared binomial

#(x+k)^2 = color(blue)(x^2+2kx)+k^2#

So if#color(blue)(x^2-6x)# are the first two terms of an expanded squared binomial, then#k=-3# and the third term must be#k^2=9# We can add

#9# to the given expression to "complete the square", but we we also need to subtract#9# so that the value of the expression stays the same.

or, in explicit vertex form:

Typically I leave the value

#m# off when it is#1# (the default anyway) but find that writing the constant term as#+(-1)# helps me remember that the#y# coordinate of the vertex is#(-1)#