Question

Please help! Can you please explain your answers so I understand? A man throws a ball off the top of a building and records the height of the ball at different times, as shown in the table.
a. find the quadratic model for the data
b. use the model to estimate the height of the ball at 2.5 seconds
c. what is the ball's maximum height?

Answer 1

Table: Time - Height
0 - 46
1 - 63
2 - 48
3 - 1

Answer 2

quadratic will be of general form h = at^2 + bt + c

at t = 0,
h = 46 = a(0)^2 + b(0) + c
so c = 46

at t = 1
h = 63 = a(1)^2 +b(1) + c = a + b + 46
a+b = 63-46

at t = 2
h = 48 = a(2)^2 + b(2) + c = 4a + 2b + 46
4a + 2b = 48-46 = 2

so now you have two equations in two unknowns, which you can solve for values of a and b.

then use t = 2.5 to find the height at that point

to find the maximum height, find the vertex of the parabola