# How do you find the vertex and the intercepts for y=-3(x+3)^2?

Jan 1, 2018

$\left(- 3 , 0\right) , - 27 , - 3$

#### Explanation:

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

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

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

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

$\text{with "h=-3" and } k = 0$

$\Rightarrow \textcolor{m a \ge n t a}{\text{vertex }} = \left(- 3 , 0\right)$

$\textcolor{b l u e}{\text{to find intercepts}}$

• " let x = 0, in the equation for y-intercept"

• " let y = 0, in the equation for x-intercepts"

$x = 0 \to y = - 3 \left(9\right) = - 27 \leftarrow \textcolor{red}{\text{y-intercept}}$

$y = 0 \to - 3 {\left(x + 3\right)}^{2} = 0$

$\Rightarrow {\left(x + 3\right)}^{2} = 0$

$\Rightarrow x + 3 = 0 \Rightarrow x = - 3 \leftarrow \textcolor{red}{\text{x-intercept}}$
graph{-3(x+3)^2 [-10, 10, -5, 5]}