Suppose a person on the surface of an asteroid kicks a ball. The table shows the height, h, in meters, of the ball over time, t, in seconds, after it is kicked into the air.

Question

t h
0
0 0
3 16.2
6 28.8
9 37.8
12 43.2
15 45
18 43.2
21 37.8
24 28.8
27 16.2
30 0

Write the quadratic relation in vertex form that models this situation.

Answer 1

since h(0)=0 and h(30)=0, the vertex must be at t=15

h(t) = 45-a(t-15)^2
45-a*15^2 = 0
225a = -45
a = -1/5

h(t) = -1/5 (t-15)^2 + 45

Answer 2

peak (vertex) at t = 15, h =45
note symmetry about t = 15

(t-15)^2 = 4a(h-45)

when t = 0, h = 0

225 = 4a (-45)

a = -5/4
(t-15)^2 = -5(h-45)

check if h = 0 at t = 30
(15)^2 =-5(h-45)
225 = -5 h +225 sure enough h = 0

Answer 3

Thank you so much guys I appreciate it!