The cabile of a suspension bridge hangs symmetrically between two towers such that it height, in feet?

Question

above the flat,horziontal road bed tht it supports is given by
h(x)=0.0032x^2-1.6x + 210.
where x is horizontal distance fromthe first twoer.
a) find the distance between thr towers, the minimum height of the cable bove the raod bed and the height of the towers above the road bed.
b)If a second road bed is buld 20 feet above the firs, where (for what x) is the cable above the upper raod bed?

I need help on this one, thank you

Answer 1

h(x) = 2(.04x-10)²+10
a) Therefore, the minimum, which is half way between the two towers is where .04x = 10 or at x = 250. Thus, the distance between the two towers is 500 feet.

b) Just subtract 20 off:
2(.04x-10)²-10