SOLUTION: The suspension cable that supports a small footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by h(x) = 0.25x2 − 0.2x +

Question 1173492: The suspension cable that supports a small footbridge hangs in the shape of a parabola. The height h, in feet, of the cable above the bridge is given by
h(x) = 0.25x2 − 0.2x + 25,
where x is the distance in feet from one end of the bridge. What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
The suspension cable that supports a small footbridge hangs in the shape of a
parabola.
The height h, in feet, of the cable above the bridge is given by
h(x) = 0.25x^2 − 0.2x + 25,
where x is the distance in feet from one end of the bridge.
What is the minimum height of the cable above the bridge? (Round your answer to two decimal places.)
:
The minimum occurs on the axis of symmetry, use x = -b/(2a) where a=.25, b=-.2
x =
x =
x = .4 is the axis of symmetry
:
Find the min, replace x with .4
h(x) = .25(.4^2) - .2(.4) + 25
h(x) = .04 - .08 + 25
h(x) = 24.96 ft is the minimum height
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