Find the eaquation for the height of the ball

Question

 Alejandra was working on physics project to track the path of the ball kicked from a hill. His   High speed camera tracked the balls height, but all all but three pictures were lost. From those three pictures, he determined that after one second, the ball is 50 feet high. After two seconds, the ball was 70 feet high, and after three seconds, the ball is 85 feet high. Assume that the height of the ball forms a parabola  

Answer 1

(1,50),(2,70),(3,85)

h=at^2 +vt +h

50 =a+v+h

v= initial velocity

h= initial height

a=twice acceleration due to gravity, a<0

70=a(2^2)+v(2)+h

70=4a +2v+h

85=9a+3v+h

50=a+v+h

3 equations, 3 unknowns

solve by substitution, elimination or matrix algebra

20=3a+v

35=8a+2v

40=6a+2v

-5=2a

a=-2.5 ft/sec^2 = deceleration due to gravity

v=20-3v=20-7.5= 12.5 ft/sec = initial upward velocity

h=50-a-v=50+2.5-12.5=40 feet high initially

h(t)= -2.5t^2 +12.5t +40