# What is the equation of the parabola that has a vertex at # (-4, 16) # and passes through point # (0,0) #?

##### 1 Answer

Feb 9, 2016

Let us solve this problem by substituing both points into a parabola equation:

#### Explanation:

- First of all, let us substitute
#(0,0)# :

Thus, we obtain the independent term in equation, getting

- Now, let us substitute the vertex,
#(-4, 16)# . We get:

Now, we have a relation between

- For any parabola, the vertex can be obtained by:

In our case:

- Finally, we must solve the system given by:

Replacing

And finally:

This way, the parabola equation is: