Question

A building has an entry the shape of a parabolic arch 52ft high and 42ft wide at the base. Find an equation for the parabola if the vertex is put at the origin of the coordinate system.

Answer 1

The description expresses three points which can be used for a standard form equation. The vertex is stated to be (0,0) and is a maximum; two other points are (-21,-74) and (21,-74)
The equation for vertex form of a parabola:
y=a(x-h)^2+k
vertex (h,k)
thus our equation will be:
y=a(x-0)^2+0
thus
y=ax^2
using one of the points, the value of a will be:
-74=a(21)^2
a=-74/441
thus the equation will be:
y=-74/441x²