if the arch height is 17.5 and the roots of the equation is x=52.5 and the parabola is symmetrical about x=0 then you are nearly right.solve a(52.5)^2-17.5=0then put the value of a you get into -ax^2+17.5=0 and you're done right?
your question doesnt really make sense. what is it you want to do and what do you have to start with? also are you doing A level or are you just mucking around?