Math
posted by Emily .
An engineer is designing a parabolic arch. The arch must be 15 m high, and 6 m wide at a height of 8 m. a) Determine a quadratic function that satisfies these conditions.
I've got : 8=a(6h)^2+15, but i don't know what to do next.

I will assume that your equation is such that the vertex is on the yaxis
Then your equation will be
y = ax^2 + 15 , (the h of your equation will be zero)
then (6,8) must lie on the equation
8 = a(6)^2 + 15
a = 7/36
equation: y = (7/36)x^2 + 15 
the peak is at 3,15, it turns downward so that at h=8 me the difference in x is 6.
h=a(x3)^+15
then
8=a(63)^2+15
8=9a+15
a=7/9
so, here is one that satisfies the statement
h=7/9 (x3)^2+15 
Bobpursley, how do you know that the peak is at (3,15)?

i don't know howto solve this either someone HELP