# How do you five the vertex and axis of symmetry f(x) = 1/3(x + 5)^2 - 1?

Nov 23, 2017

$\left(- 5 , - 1\right) \text{ and } x = - 5$

#### Explanation:

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

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

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

$f \left(x\right) = \frac{1}{3} {\left(x + 5\right)}^{2} - 1 \text{ is in vertex form}$

$\text{with "h=-5" and } k = - 1$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 5 , - 1\right)$

$\text{the axis of symmetry passes through the vertex is}$
$\text{vertical and has equation}$

$x = - 5$
graph{(y-1/3x^2-10/3x-22/3)(y-1000x-5000)=0 [-10, 10, -5, 5]}