Parabola Application Questions
Sunfire is a glass parabola used to collect solar energy. The sun’s
rays are reflected from the mirrors toward two boilers located at
the focus of the parabola. When heated, the boilers produce
steam that powers an alternator to produce electricity.
a. Write an equation for Sunfire’s cross section.
b. How deep is the dish?
y = a(x – h)2 + k
y = a(x – 0)2 + 0
y = ax2
p = 10
1
a= =
y=
4𝑝
1 2
x
40
1
4(10)
=
1
40
y=
1 2
x
40
1
(18.5)2
40
y=
y = 8.556 feet
The satellite dish is 8.556 feet deep.
A concrete bridge is designed with an arch in the shape of a
parabola. The road over the bridge is 120 feet long and the
maximum height of the arch is 50 feet. Write an equation for
the parabolic arch. How far above the water is the bridge 10
feet from the shore?
y = a(x – h)2 + k
y = a(x – 60)2 + 50
The point (0,0) represents
the end of the bridge.
0 = a(0 – 60)2 + 50
0 = 3600a + 50
−1
-50 = 3600a
2 + 50
y
=
(x
–
60)
−50
−1
72
a=
=
3600 72
y = 15.27
The bridge has a height of 15.27 feet
−1
y = (x – 60)2 + 50
when 10 feet from the shore.
72