# What is the equation of the parabola that has a vertex at  (3, -6)  and passes through point  (-9,7) ?

Mar 5, 2018

$f \left(x\right) = \frac{13}{144} {\left(x - 3\right)}^{2} - 6$

#### Explanation:

We know that

$f \left(x\right) = a \cdot {\left(x - 3\right)}^{2} - 6$

because of the vertex at $\left(3 , - 6\right)$. Now we have to determinated $a$ by plugging in the point $\left(- 9 , 7\right)$.

$7 = a \cdot {\left(- 9 - 3\right)}^{2} - 6$

In order to find $a$, we solve for $a$

$7 = a \cdot {\left(- 9 - 3\right)}^{2} - 6 | + 6$
13=144a|:144
$\frac{13}{144} = a \approx 0.09$