The difference, I'll call d, vertically between the functions is:
d=x+56-x^2
Now we can take the derivative of d with respect to x:
dd/dx=-2x+1
dd/dx=0 when -2x+1=0, x=1/2
d(1/2)=x+56-x^2=56.25
Now you can check the endpoints just in case...
d(-7)=0 and d(8)=-16
So the maximum vertical distance of 56.25 units occurs when x=1/2
