# How do you find the vertex of y=2(x+4)^2-7?

May 4, 2017

$\left(- 4 , - 7\right)$

#### Explanation:

$\text{the equation of a parabola in "color(blue)"vertex form}$ is.

$\textcolor{red}{\overline{\underline{| \textcolor{w h i t e}{\frac{2}{2}} \textcolor{b l a c k}{y = a {\left(x - h\right)}^{2} + k} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

$\text{where " (h,k)" are the coordinates of the vertex }$
$\text{and a is a constant}$

$y = 2 {\left(x + 4\right)}^{2} - 7 \text{ is in this form}$

$\text{with " h=-4" and } k = - 7$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 4 , - 7\right)$

May 4, 2017

The standard vertex form form is:

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

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

#### Explanation:

Change the given equation,

$y = 2 {\left(x + 4\right)}^{2} - 7$

into the form of equation [1] by changing the plus sign into two minus signs:

$y = 2 {\left(x - - 4\right)}^{2} - 7 \text{ [2]}$

Matching equation [2] with equation [1], we can see that the vertex is, $\left(- 4 , - 7\right)$