Question

A building has an entry the shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown below.

Answer 1

The equation of a parabola with vertex at (h,k) is 
y=a(x-h)²+k

vertex isi at (0,0)

y=a(x-0)²+0
y=a(x)²
y=ax²
find a

we see that one point is (14,-74)
x=14 and y=-74

-74=a(14²)
-74=196a
divide both sides by 196
-37/98=a

the equation is 

$y= \frac{-37}{98} x^2$

Answer 2

If a building has an entry shape of a parabolic arch 74 ft high and 28 ft wide at the base as shown in the figure and then the vertex is at (0,0). The parabola is opening downward, so the equation to be used is x² = -4ay.  4a is equal to 28 and so the equation is x² = -28y