Write a quadratic function from its vertex and another point

The graphing form for a parabolic function is:  y - k  =  a(x - h)²  where  (h, k)  is the vertex.

 

For this problem:  (h, k)  =  (0, 0)  so  h = 0  and  k = 0.

Placing these values into:  y - k  =  a(x - h)² 

we get:                               y - 0  =  a(x - 0)²

or:                                           y   =  a·x²

 

We are also given that this parabola passes through the point (12, -9).

This means that we can replace  x  with  12  and  y  with  -9.

--->   y   =  a·x²​   --->    -9  =  a·12²   --->   -9  =  144a   --->   a  =  -9/144   --->   a  =  -1/16

 

So, the equation is:  y  =  (-1/16)x²