# How do you find the equation of the parabola with vertex (-3, 1) and passing thru (-5, -11) if its axis of symmetry is parallel to the Y-axis?

Oct 26, 2017

$y = - 3 {x}^{2} - 18 x - 26$

#### Explanation:

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

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

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

$\text{here } \left(h , k\right) = \left(- 3 , 1\right)$

$\Rightarrow y = a {\left(x + 3\right)}^{2} + 1$

$\text{to find a substitute "(-5,-11)" into the equation}$

$- 11 = 4 a + 1 \Rightarrow 4 a = - 12 \Rightarrow a = - 3$

$\Rightarrow y = - 3 {\left(x + 3\right)}^{2} + 1 \leftarrow \textcolor{red}{\text{ in vertex form}}$

$\text{distributing and simplifying gives}$

$y = - 3 {x}^{2} - 18 x - 26 \leftarrow \textcolor{red}{\text{in standard form}}$
graph{-3x^2-18x-26 [-11.25, 11.25, -5.625, 5.625]}