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Suppose that you are an engineer designing an arch bridge spanning the entrance to a marina. Small watercraft will be passing under the bridge, so it is important to allow for proper clearance. The arch will be 120 feet wide at its base and 40 feet tall at its peak. In a rectangular coordinate system, the feet of the arch will be at (-60, 0) and (60, 0) and the peak will be at (0, 40). In this activity, you will compare two different shapes for the arch described. 1. If the arch were parabolic in shape, it would have an equation of the form y = ax² + c. Use the coordinates given above to write an equation of a parabolic arch with the given dimensions. Write the value of a as a simplified fraction. 2. Use your equation from #1 to find the height of the arch at distances of 10 feet, 20 feet, 30 feet, 40 feet, and 50 feet from the center. Round to the nearest foot. Organize your results in the table. Then draw the arch in a rectangular coordinate system. Distance from Center Height 10 feet 20 feet 30 feet 40 feet 50 feet

Suppose that you are an engineer designing an arch bridge spanning the entrance to a marina. Small watercraft will be passing under the bridge, so it is important to allow for proper clearance. The arch will be 120 feet wide at its base and 40 feet tall at its peak. In a rectangular coordinate system, the feet of the arch will be at (-60, 0) and (60, 0) and the peak will be at (0, 40). In this activity, you will compare two different shapes for the arch described. 1. If the arch were parabolic in shape, it would have an equation of the form y = ax² + c. Use the coordinates given above to write an equation of a parabolic arch with the given dimensions. Write the value of a as a simplified fraction. 2. Use your equation from #1 to find the height of the arch at distances of 10 feet, 20 feet, 30 feet, 40 feet, and 50 feet from the center. Round to the nearest foot. Organize your results in the table. Then draw the arch in a rectangular coordinate system. Distance from Center Height 10 feet 20 feet 30 feet 40 feet 50 feet

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018
18th Edition
ISBN:9780079039897
Author:Carter
Publisher:Carter
Chapter9: Quadratic Functions And Equations
Section9.7: Solving Systems Of Linear And Quadratic Equations
Problem 14PPS
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Suppose that you are an engineer designing an arch bridge spanning the entrance to a marina. Small watercraft will be passing under the bridge, so it is important to allow for proper clearance. The arch will be 120 feet wide at its base and 40 feet tall at its peak. In a rectangular coordinate system, the feet of the arch will be at (-60, 0) and (60, 0) and the peak will be at (0, 40). In this activity, you will compare two different shapes for the arch described. 1. If the arch were parabolic in shape, it would have an equation of the form y = ax² + c. Use the coordinates given above to write an equation of a parabolic arch with the given dimensions. Write the value of a as a simplified fraction. 2. Use your equation from #1 to find the height of the arch at distances of 10 feet, 20 feet, 30 feet, 40 feet, and 50 feet from the center. Round to the nearest foot. Organize your results in the table. Then draw the arch in a rectangular coordinate system. Distance from Center Height 10 feet 20 feet 30 feet 40 feet 50 feet
Transcribed Image Text:Suppose that you are an engineer designing an arch bridge spanning the entrance to a marina. Small watercraft will be passing under the bridge, so it is important to allow for proper clearance. The arch will be 120 feet wide at its base and 40 feet tall at its peak. In a rectangular coordinate system, the feet of the arch will be at (-60, 0) and (60, 0) and the peak will be at (0, 40). In this activity, you will compare two different shapes for the arch described. 1. If the arch were parabolic in shape, it would have an equation of the form y = ax² + c. Use the coordinates given above to write an equation of a parabolic arch with the given dimensions. Write the value of a as a simplified fraction. 2. Use your equation from #1 to find the height of the arch at distances of 10 feet, 20 feet, 30 feet, 40 feet, and 50 feet from the center. Round to the nearest foot. Organize your results in the table. Then draw the arch in a rectangular coordinate system. Distance from Center Height 10 feet 20 feet 30 feet 40 feet 50 feet
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