# How do you rewrite y = x^2 + 14x + 29 in vertex form?

Nov 26, 2017

$y = {\left(x + 7\right)}^{2} + 20$

#### Explanation:

Given -

$y = {x}^{2} + 14 x + 29$

Vertex form of the equation is -

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

Where -

$a -$ is the coefficient of ${x}^{2}$
$h -$ is the x-coordinate of the vertex
$k -$ is the y-coordinate of the vertex

First, find the vertex of the given equation

$x = \frac{- b}{2 a} = \frac{- 14}{2} = - 7$

$y = {\left(- 7\right)}^{2} + 14 \left(- 7\right) + 29 = 49 - 98 + 29 = - 20$

Vertex $\left(- 7 , - 20\right)$

$a = 1$

Substitute these values in the formula

$y = {\left(x - \left(- 7\right)\right)}^{2} - \left(- 20\right)$

$y = {\left(x + 7\right)}^{2} + 20$

Nov 26, 2017

$y = {\left(x + 7\right)}^{2} - 20$

#### Explanation:

Vertex form is $y = a {\left(x + b\right)}^{2} + c$

Use the process of completing the square

$y = {x}^{2} + 14 x \textcolor{red}{+ {7}^{2} - {7}^{2}} + 29 \text{ } \leftarrow \textcolor{red}{{\left(\pm \frac{14}{2}\right)}^{2}}$

$y = \left({x}^{2} + 14 x + 49\right) + \left(- 49 + 29\right)$

$y = {\left(x + 7\right)}^{2} - 20$

This is vertex form.

The vertex will be at $\left(- 7 , - 20\right)$