EXAMPLE
Student Help
STUDY TIP
Golden Gate
Bridge, Highway and
Transportation District
Points on a Parabola
The main suspension cables of the Golden Gate Bridge form a parabola
that can be modeled by the quadratic function
The lowest point of the
main cables at the
midpoint is about 8 feet
above the roadway.
䊳 Source:
3
y 0.000112x2 8
where x is the horizontal distance from the middle of the bridge (in feet) and
y is the vertical distance from the road (in feet).
The cables are connected to the towers at points that are 500 feet above the
road. How far apart are the towers?
y
500 ft
500 ft
x
Not drawn to scale
Solution
You can find the distance between the towers by finding the x-values for which
y 500, or 0.000112x2 8 500. Use a graphing calculator to find the
solutions of the equation.
Write the equation in the standard form ax2 bx c 0.
0.000112x2 8 500
0.000112x2 492 0
Write original equation.
Subtract 500 from each side.
Sketch the graph of the related quadratic function
y 0.000112x 2 492 using a graphing
calculator.
Estimate the values of the x-intercepts. From the
graphing calculator screen, you can see that the
x-intercepts are approximately 2100 and 2100.
Each tower is approximately 2100 feet from the
midpoint. Because the towers are on opposite sides
of the midpoint, the distance between the towers is
2100 2100 4200.
ANSWER 䊳
The towers are approximately 4200 feet apart.
Points on a Parabola
4.
528
Chapter 9
The main suspension cables of the Royal Gorge Bridge can be modeled
by the quadratic function y 0.0007748x2. In the equation, x is the
horizontal distance from the middle of the bridge (in feet) and y is the
vertical distance from the road (in feet). The cables are connected to the
towers at points that are 150 feet above the road. Approximately how far
apart are the towers?
Quadratic Equations and Functions