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) = 0.25x^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 = {{{(-(-.2))/(2*.25)}}}
x = {{{.2/.5}}}
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