Question

An engineer is desingning a parabloic arch, the arch must be 15 m high , and 6 m wide, at a height of 8 m

a) determine a quadratic fundtion that satisfies these conditions

b) what is the width of the arch at its base

Answer 1

Let the arch be centered on the y-axis. Then the equation will be
y = -ax^2 + k

It will have height 6 at x = 3 and -3
The vertex will be at (0,15)

y = -ax^2 + 15
6 = -a(3^2) + 15
6 = -9a + 15
-9 = -9a
a = 1

y = -x^2 + 15

y=0 when x^2 = 15, so the width is 2√15 at its base

Answer 2

Roof of a tunnel is in the shape of parabolic arch whose highest point is 18m above a road. The road surface is 16m wide at ground level. Lights are placed in the tunnel 12 m high. How far from the center of the tunnel are the lights placed?