Question

17) A baseball coach records the height at every second of a ball thrown in the air. Some of the data points

appear in the table below: Which equation is a quadratic model for the data?
Time (s)
0
1
3
Height (ft)
0
64
96
A) h = -16t? + 80t
B)h = -48t2 + 112t
C) h = -32t2 + 80t
D) = -16t2 + 640

Answer 1

The equation of the quadratic model for the data is h = -16t² + 80t

Which equation is a quadratic model for the data?

From the question, we have the following parameters that can be used in our computation:

The table of values

A quadratic equation is represented as

h = at² + bt + c

Where

c = y when t = 0

So we have

h = at² + bt

Using the points on the table, we have

a + b = 64

9a + 3b = 96

When evaluated, we have

3a + 3b = 192

9a + 3b = 96

------------------

-6a = 96

This gives

a = -16

Recall that

a + b = 64

So, we have

b = 64 + 16

b = 80

Hence, the equation of the quadratic model for the data is h = -16t² + 80t