Quadratics question

Question

A man kicks a soccer ball from 5metres from the goal line. The ball goes 15metres high and 38 metres far.

Using either factored or vertex form. Find the equation of this quadratic. (Round to three decimal places)

Answer 1

f(5) = 0 ----> 25A + 5B + C = 0

f(38) = 0 ---> 1444A + 38B + C = 0

f(22)=15 ---> 484A + 22B + C = 15

Subtracts Equation 2 - Equation 1:

1419A + 33B = 0

Subtracts Equation 2 - Equation 3:

960A + 16B = -15

Solves by Elimination

-16 ( 1419A + 33B) = 0

33 ( 960A + 16B ) = -495

-22704A + -528B = 0

31680A + 528B = -495

8976A = -495

A = -495/8976 = -15/272

1419(-15/272) + 33B = 0

1419*(-15) + 272*33 B = 0

-21285 + 8976B = 0

B = 21285/8976 = 645/272

25 ( -15/272) + 5( 645/272) + C = 0

25 * -15 + 5 * 645 + 272C = 0

272C + 2850 = 0

C = -2850/272 = -1425/136

The quadratic function is:

f(x) = (-15/272) x^2 + (645/272) x - (1425/136)