# What is the equation of the parabola that has a vertex at # (10, 8) # and passes through point # (5,83) #?

##### 1 Answer

May 28, 2017

Actually, there are two equations that satisfy the specified conditions:

A graph of both parabolas and the points is included in the explanation.

#### Explanation:

There are two general vertex forms:

where

This gives us two equations where "a" is unknown:

To find "a" for both, substitute the point

The two equations are:

Here is a graph that proves that both parabolas have the same vertex and intersect the required point: