SOLUTION: The drama club is building a backdrop using arches whose shape can be represented by the function f(x) = -x^2 + 2x + 8, where x is the length in feet. The area under each arch is t

Question 1038139: The drama club is building a backdrop using arches whose shape can be represented by the function f(x) = -x^2 + 2x + 8, where x is the length in feet. The area under each arch is to be covered with fabric.
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What is the height of the arch?
10 feet
9 feet
8 feet
6 feet
Found 2 solutions by Alan3354, Boreal:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
y = -x^2 + 2x + 8
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The high point is the vertex.
The vertex is on the LOS, the Line of Symmetry.
The LOS equation is x = -b/2a
x = -2/-2 = 1
y at x = 1 --> -1 + 2 + 8
= 9 feet

Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
-x^2+2x+8
The vertex is at -b/2a and the x value is -2/-2 or 1. The y-value is -1+2+8=9
The y-intercept is at (0,8)

The vertex is 9 feet from the floor or the y-axis in this instance.
Other questions ask about the floor space under the arch, and that is 6 feet, judging by the x-intercepts.
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