How do you write the equation of the parabola in vertex form given vertex(0,3) point (-4,-45)?

Apr 12, 2018

$y = - 3 {x}^{2} + 3$

Explanation:

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

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

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

$\text{here } \left(h , k\right) = \left(0 , 3\right)$

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

$\textcolor{w h i t e}{\Rightarrow y} = a {x}^{2} + 3$

$\text{to find a substitute "(-4,-45)" into the equation}$

$- 45 = 16 a + 3 \Rightarrow 16 a = - 48 \Rightarrow a = - 3$

$\Rightarrow y = - 3 {x}^{2} + 3$