An engineer is designing a parabolic arch. the arch must be 15 m high, and 6 m wide at the height of 8 m. determine a quadratic function that satisfies these conditions.

Let's assume we've got our maximum at 0 (this simplifies things). We need f(0)=15.
Also, to make it 6m wide at a height, we have to set f(3)=8 and f(-3)=8. Now we have:

We could easily notice that b=0 and c=15, let's find a: 9a+15=8 or 9a=-7 or
The function is