Example 7
The Golden Gate Bridge in San Francisco is one of the most internationally recognized bridges in the world. When it was built in 1937, it had the longest suspension bridge span in the world. The shape of the main suspension cable is a parabola that is more than one mile in length. The road across the bridge is 246 above the water level. The two towers are 746 feet above the water level, and are 4 200 feet apart. The lowest point of the cable is 10 feet above the road.
road
road
A Cartesian plane (grid) is superimposed on the diagram with the origin at the top of the left tower.
a) State the coordinates of the top of each tower and the vertex of the parabola.
b) Determine the equation of the parabola in general form.
c) State a suitable window for graphing the equation on your calculator. Verify the coordinates of the vertex.
d) Determine the height of the cable above the road, 900 feet from the left tower.
e) The equation of the parabola can also be written in standard form. Determine the equation.
Example 8
The cross section of a satellite dish is parabolic with measurements as shown in the diagram.
A Cartesian plane is to be superimposed on the diagram with the origin at the vertex of the parabola. a) Determine the equation of this parabola in standard form.
14 cm
8 cm
6 cm
(0, 0)
b) If the maximum depth of the dish is 8 cm, determine the width of the dish to the nearest tenth of a centimetre.
Determine the equation of each quadratic.
Example 3
b) The data looks like it could be modeled by a quadratic function. A teacher is able to determine that the equation that best models this data is
Use the model to determine what speed, to the nearest kilometre, results in the lowest cost per kilometre.
c) Determine the lowest cost per kilometre. Answer to the nearest tenth.
d) Based on this model, which speed is more likely to cost more, 25 km/h or 125 km/h?
Example 2
see p. 348 ­ Class Ex #2
Example 5 A rectanglular lot is bounded on one side by a river and on the other side by a fence. The three sides of fencing have a total of 80 m in length. a) Using l for length and w for width, determine an equation for the following:
i) perimeter
ii) width
iii) area
b) Determine the length and width of the fenced area which will result in maximum area.
Example 6
Two numbers differ by 8 and have a product that is a minimum. Determine the two numbers.
p. 358 #s 1, 3, 4, 5, 6