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

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) (Show Source): You can put this solution on YOUR website!

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

.

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.

ANSWER a: The equation of the parabola is

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

= 6.148 feet to 3 decimal places

ANSWER b: about 6.148 feet

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