A road is made in such a way that the center of the road is higher off the ground than the sides of the road, in order to allow
rainwater to drain. A cross-section of the road can be represented on a graph using the function f(x) = -1/200(x – 16)(x + 16), where x represents the distance from the center of the road, in feet. Rounded to the nearest tenth, what is the maximum height of the road, in feet?
2 answers:
Remark.
The problem is a bit indistinct. Where exactly are the two edges of the road? I'm going to say that they are the x intercepts, but that may not be true. Certainly it does not have to be true at all.
Graph.
A graph has been made for you. The maximum is marked for you. It is an approximation The actual height can be more accurately found.
Height
y = (-1/200)(x - 16)(x + 16)
y = (-1/200)*(x^2 - 256)
The maximum height for this graph only is when x = 0.Other graphs require completing the square.
y = (-1/200) * (-256)
y = 1.28 exactly. I thought the graph might be rounding the answer. It is not.
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