Question

A building has an entry the shape of a parabolic arch 96 ft high and 18 ft wide at the base as shown below.

Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

i think the answer is??
y = a(x - 0)^2 + 0

the point is (9, -96);
-96 = a(9^2) = 81a

a = -96/81 = -32/27

y = (-32/27)x^2

y = (-32/27)(x - 0)^2 + 0