# What is the equation of the parabola that has a vertex at  (7, 9)  and passes through point  (3, -2) ?

Dec 30, 2015

It is easiest to use the form y = a${\left(x - p\right)}^{2}$ + q

#### Explanation:

In vertex form, the form mentioned above, The vertex is represented by (p, q) and the of your choice is represented by X and Y respectively. In other words you are solving for a in the formula.

-2 = a${\left(3 - 7\right)}^{2}$ + 9
-2 = 16a + 9
-2 -9 = 16a
$- \frac{11}{16}$ = a

So, the equation would be y = $- \frac{11}{16}$${\left(x - 7\right)}^{2}$ +9