The cable of a suspension bridge hangs in the shape of a parabola. The towers supporting the cable are $400$ ft apart and $150$ ft high. If the cable, at its lowest is $30$ ft above the bridge at its midpoint, how high is the cable $50$ ft away (horizontally) from either tower?
I tried the formula $y^2=4cx$ and $x^2=4cx$ but I still don't know the answer. I'm confused.
Find $a$ in the parabola form:
$$ k= 30, \;y(x)-k = a x^2 \,@ (x= 200,y=150) $$
Next find $$ y(x) @ x=\pm(200-50) $$