How do you write the equation of the parabola in vertex form given the vertex (9,-2) and point (12,16)?

Apr 2, 2016

$y = 2 {\left(X - 9\right)}^{2} - 2$

Explanation:

The general vertex form is
$\textcolor{w h i t e}{\text{XXX}} y = m {\left(x - a\right)}^{2} + b$ for a parabola with vertex at $\left(a , b\right)$

So a parabola with vertex at $\left(9 , - 2\right)$ will have the form:
$\textcolor{w h i t e}{\text{XXX}} y = m {\left(x - 9\right)}^{2} + \left(- 2\right)$

Since $\left(x , y\right) = \left(12 , 16\right)$ is given as a solution to this equation
$\textcolor{w h i t e}{\text{XXX}} 16 = m {\left(12 - 9\right)}^{2} - 2$

$\textcolor{w h i t e}{\text{XXX}} 16 = 9 m - 2$

$\textcolor{w h i t e}{\text{XXX}} m = 2$
and
the equation of the parabola is
$\textcolor{w h i t e}{\text{XXX}} y = 2 {\left(x - 9\right)}^{2} - 2$
graph{2(x-9)^2-2 [1.37, 13.854, -2.37, 3.87]}