The main cable of a suspension bridge forms a parabola modeled by the equation y is equal to A times open paren x minus h close paren squared plus k where y is the height in feet of the cable above the road, x is the horizontal distance in feet from the right bridge support, A is a constant, and open paren h comma k close paren is the parabola’s vertex. What is the maximum and minimum height of the bridge modeled by the equation y is equal to 0 point 0 0 5 times open paren x minus 60 close paren squared plus 8 ?
Answer
A
maximum height is equal to 26 feet and minimum height is equal to 8 feet
B
maximum height is equal to 100 feet and minimum height is equal to 26 feet
C
maximum height is equal to 60 feet and minimum height is equal to 26 feet
D
maximum height is equal to 100 feet and minimum height is equal to 8 feet
Explanation
The coefficient 0.005 is positive, so the parabola opens upward and its vertex gives the minimum height. The vertex is (60, 8), so the minimum is 8 feet. At either support, 60 feet horizontally from the vertex, the height is 0.005(60)² + 8 = 26 feet, which is the maximum on the bridge. Thus, the correct choice is “maximum height is equal to 26 feet and minimum height is equal to 8 feet.”
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