Unit: Quadratics section: max/min word problems

i have no idea how to do this problem:
A soccer ball lying on the ground is kicked downfield and hits the ground 62m away. If the max. height reached by the ball is 15m, algebraically determine the quadratic function that models this trajectory and use the function to calculate the height when it is 48m downfield.

The answer is : y= - 15/931(x-31)^2+15
height= 10.5m at 48 m downfield

( ^2 means to the power of 2 )

My test is tomorrow so much help quickly would be greatlyy appreciated!!!

2. Originally Posted by kaitlynmary
Unit: Quadratics section: max/min word problems

i have no idea how to do this problem:
A soccer ball lying on the ground is kicked downfield and hits the ground 62m away. If the max. height reached by the ball is 15m, algebraically determine the quadratic function that models this trajectory and use the function to calculate the height when it is 48m downfield.

The answer is : y= - 15/931(x-31)^2+15
height= 10.5m at 48 m downfield

( ^2 means to the power of 2 )

My test is tomorrow so much help quickly would be greatlyy appreciated!!!
Use the model $\displaystyle y = a(x - h)^2 + k$.

Assuming the ball is kicked from (0, 0), you know that the turning point is at (31, 15) (why is the x-coordinate equal to 31?) and therefore you know the value of h and k. Furthermore, you know that (62, 0) is on the curve so you can find the value of a.