Question

Determining the Regression Equation
The table below shows the approximate height of a ball thrown up in the air after x seconds.

A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 1, 2, 3, 4. The second column is labeled height (feet) with entries 5, 90, 140, 160, 150.
Which quadratic model best represents the data?

f(x) = –16x2 + 99x + 6
f(x) = –36x2 + 37x + 5
f(x) = 36x2 + 37x + 5
f(x) = 16x2 + 99x + 6

Answer 1

f(x) = –16x^2 + 99x + 6.

Reason: gravity gives a -16x^2 term (feet, seconds). Checking the table:
- f(0)=6 ≈ 5
- f(1)= -16+99+6 = 89 ≈ 90
- f(2)= -64+198+6 = 140 (matches)
- f(3)= -144+297+6 = 159 ≈ 160
- f(4)= -256+396+6 = 146 ≈ 150

This model fits the data closely.