# What is the vertex form of y=x^2 - 4x + 14 ?

Mar 19, 2016

$y = 1 {\left(x - 2\right)}^{2} + 10$

#### Explanation:

Complete the square to rearrange into vertex form:

$y = {x}^{2} - 4 x + 14$

$= {x}^{2} - 4 x + 4 + 10$

$= {\left(x - 2\right)}^{2} + 10$

$= 1 {\left(x - 2\right)}^{2} + 10$

The equation:

$y = 1 {\left(x - 2\right)}^{2} + 10$

is in the form:

$y = a {\left(x - h\right)}^{2} + k$

which is the equation of a parabola with vertex at $\left(h , k\right) = \left(2 , 10\right)$ and multiplier $1$.