# How do you write the equation of the parabola in vertex form given vertex (–4, 7) and also passes through the point (–3, 8)?

Jul 30, 2018

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

#### Explanation:

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

•color(white)(x)y=a(x-h)^2+k

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

$\text{here "(h,k)=(-4,7)" hence}$

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

$\text{to find a substitute "(-3,8)" into the equation}$

$8 = a + 7 \Rightarrow a = 8 - 7 = 1$

$y = {\left(x + 4\right)}^{2} + 7 \leftarrow \textcolor{red}{\text{in vertex form}}$