SOLUTION: An arch is in the shape of a parabola. It has a span of 240 feet and a maximum height of 30 feet. a. Find the equation of the parabola (assuming the origin is halfway between th

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: An arch is in the shape of a parabola. It has a span of 240 feet and a maximum height of 30 feet. a. Find the equation of the parabola (assuming the origin is halfway between th      Log On


   

Question 1204029: An arch is in the shape of a parabola. It has a span of 240 feet and a maximum height of 30 feet.
a. Find the equation of the parabola (assuming the origin is halfway between the arch's feet).
b. Determine the height of the arch 107 feet from the center.
Answer by greenestamps(13200) About Me  (Show Source):
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With the origin halfway between the arch's feet and a maximum height of 30 feet, the vertex of the parabola is (0,30); the equation of the parabola is

y=-ax%5E2%2B30.

With a distance of 240 feet between the arch's feet, two points on the parabola are (120,0) and (-120,0). Use either of those two points to find the coefficient a.

0=-a%28120%29%5E2%2B30
14400a=30
a=30%2F14400=1%2F480

ANSWER a: The equation of the parabola is y=-%281%2F480%29x%5E2%2B30

Find the height of the arch 107 feet from the center by finding y when x is 107:

-%281%2F480%29%28107%5E2%29%2B30 = 6.148 feet to 3 decimal places

ANSWER b: about 6.148 feet