Question 911710
Your bungee chord description is confusing.  The equation for the arch can be formed.


The arch is based on {{{y=ax^2}}} and {{{a<0}}}.  The vertex has been moved to {{{x=275/2}}} and {{{y=290}}}.



{{{f(x)=a(x-275/2)^2+290}}}, and one of the x-intercepts is (0,275).



{{{a(x-275/2)^2+290=f(x)}}}


{{{a(x-275/2)^2=f(x)-290}}}


{{{a=(f(x)-290)/(x-275/2)^2}}}


Substitute the point

{{{a=(275-290)/(275-275/2)^2}}}


{{{a=(-15)/(18906&1/4)}}}


{{{a=-(60/75625)}}}


{{{highlight_green(a=-12/15125)}}}


Using integers as much as possible,
{{{highlight(f(x)=-(12/15125)(x-275/2)^2+290)}}}, for the arch.