Posted by Sophie on .
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

Math 
Steve,
Let the arch be centered on the yaxis. 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 
Math 
stephen,
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?