# How do you write the equation of the parabola in vertex form given vertex (–3, –4) and point (–5, 0)?

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#### Explanation:

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Jim G. Share
Feb 9, 2018

$y = {\left(x + 3\right)}^{2} - 4$

#### Explanation:

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

"color(red)(bar(ul(|color(white)(2/2)color(black)(y=a(x-h)^2+k)color(white)(2/2)|)))

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

$\text{here } \left(h , k\right) = \left(- 3 , - 4\right)$

$\Rightarrow y = a {\left(x + 3\right)}^{2} - 4$

$\text{to find a substitute "(-5,0)" into the equation}$

$0 = 4 a - 4 \Rightarrow a = 1$

$\Rightarrow y = {\left(x + 3\right)}^{2} - 4 \leftarrow \textcolor{red}{\text{in vertex form}}$

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