Question

The table below shows the height of a ball x seconds after being kicked.

A 2-column table with 5 rows. The first column is labeled time (seconds) with entries 0, 0.5, 1, 1.5, 2, 2.5, 3. The second column is labeled height (feet) with entries 0, 35, 65, 85, 95, 100, 95.
What values, rounded to the nearest whole number, complete the quadratic regression equation that models the data?

f(x) =
x2 +
x + 0
Based on the regression equation and rounded to the nearest whole number, what is the estimated height after 0.25 seconds?

feet

Answer 1

The quadratic regression (rounded to the nearest whole number) is

f(x) = -16 x^2 + 81 x + 0.

Using this, f(0.25) = -16(0.25)^2 + 81(0.25) ≈ 19.25, which rounds to 19 feet.