Question

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: evaluating this model gives f(1)=89 (~90), f(2)=140 (exact), f(3)=159 (~160), f(4)=146 (~150) — the closest match to the table values of the four choices.