The graph of f(x) = –0.01x2 + x can be used to model the height in feet of a curved arch support for a bridge, where the x-axis represents the water level and x represents the distance in feet from where the arch support enters the water. Find the height of the highest point of the bridge.
Michael
Favorite Answer
f(x) = –0.01x² + x
As the coefficient on the x² term is negative, this is a parabola that opens down.
Therefor the vertex is a maximum.
From the quadratic formula the x coordinate of the vertex is
x = -b/2a
x = -1/(2 * -.01)
x = -1/(-.02)
x = 50
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At x = 50
f(50) = -0.01(50)² + 50
f(50) = -25 + 50
f(50) = 25
The highest point is 25 feet <––––––
http://goo.gl/y49sTR
DWRead
² can be represented by ^2.
f(x) = -0.01x² + x
= -0.01(x² - 100x)
= -0.01(x² - 100x + 50²) + 0.01·50²
= -0.01(x - 50)² + 25
This is the equation for a down-opening parabola with vertex (50,25). The highest point of the bridge is 25 ft.