# What is the equation of the parabola that has a vertex at  (0, 16)  and passes through point  (2,20) ?

May 27, 2018

The equation is $y = {x}^{2} + 16$

#### Explanation:

Recall vertex form of a parabola is given by

$y = a {\left(x - p\right)}^{2} + q$

Where $\left(p , q\right)$ is the vertex and $\left(x , y\right)$ is a point which the parabola passes though. Therefore, we have enough information to solve for $a$.

$20 = a {\left(2 - 0\right)}^{2} + 16$

$4 = a \left(4\right)$

$a = 1$

Therefore the equation of the parabola is $y = {x}^{2} + 16$.

Hopefully this helps!