# What is the vertex form of y = x^2 -14x + 16?

Mar 14, 2018

$y = {\left(x - 7\right)}^{2} - 33$

#### Explanation:

First find the vertex using the formula
$x = \frac{- b}{\text{2a}}$

a=1
b=-14
c=16

$x = \frac{- \left(- 14\right)}{\text{2(1)}}$ This simplifies to $x = \frac{14}{\text{2}}$ which is 7.
so $x = 7$

So on now that we have x we can find y.

$y = {x}^{2} - 14 x + 16$
$y = {\left(7\right)}^{2} - 14 \left(7\right) + 16$
$y = - 33$

$V e r t e x = \left(7 , - 33\right)$ where h=7 and k=-33

We now finally enter this into vertex form which is,
$y = a {\left(x - h\right)}^{2} + k$

x and y in the "vertex form" are not associated with the values we found earlier.

$y = 1 {\left(x - 7\right)}^{2} + \left(- 33\right)$
$y = {\left(x - 7\right)}^{2} - 33$