The top of an arched window is modeled by the function A(x) = -x^2 + 8x - 7, where...
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Problem
The top of an arched window is modeled by the function A(x) = -x^2 + 8x - 7, where x is the horizontal distance from the left edge of the wall, in feet, and A is the distance of the arch from the floor in feet. Part A: What is the vertex of the function? Part B: How high above the floor is the top of the window?
Step-by-step solution
For Part A, the x-coordinate of the vertex is $-b/(2a) = -8/(2*(-1)) = 4$. The y-coordinate is $A(4) = -(4)^2 + 8(4) - 7 = -16 + 32 - 7 = 9$. For Part B, the height is the y-coordinate of the vertex.
Answer
(4, 9)