An arch in a memorial park, having a parabolic shape, has a height of 25 feet and a base width of 30 feet. Find an equation which models this shape, using the x-axis to represent the ground. State the focus and directrix.

Solution:

The equation is y=Ax^2+25

It passes (0,25) and (-15,0) and (15,0)

0=A*15^2+25

A = -1/9

So the equation is y=-1/9x^2+25

The focus is (0,20.5), the directrix is y=29.5