# How do you find the vertex of y = 5(x+2)^2 + 7?

May 1, 2017

The vertex form of a parabola of this type is:

$y = a {\left(x - h\right)}^{2} + k \text{ [1]}$

where $\left(h , k\right)$ is the vertex.

#### Explanation:

Given:

$y = 5 {\left(x + 2\right)}^{2} + 7 \text{ [2]}$

We can convert equation [2] into the same form as equation [1] by writing $+ 2 \text{ as} - - 2$:

$y = 5 {\left(x - - 2\right)}^{2} + 7 \text{ [3]}$

We observe that the vertex is $\left(- 2 , 7\right)$