Question

the table below shows the height of a ball x seconds after being kicked.
time (seconds) | height (feet)
0 | 0
0.5 | 35
1 | 65
1.5 | 85
2 | 95
2.5 | 100
3 | 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

Explanation:

Step1: Use a calculator for quadratic regression

Input the data points \((x = 0,y = 0)\), \((x=0.5,y = 35)\), \((x = 1,y=65)\), \((x=1.5,y = 85)\), \((x = 2,y=95)\), \((x=2.5,y = 100)\), \((x = 3,y=95)\) into a graphing - calculator or statistical software for quadratic regression. The general form of a quadratic function is \(y=ax^{2}+bx + c\). After performing the quadratic regression, we get \(a\approx - 15\), \(b\approx 80\).

Step2: Substitute \(x = 0.25\) into the regression equation

The regression equation is \(f(x)=-15x^{2}+80x\). Substitute \(x = 0.25\) into the equation:

$$
LATEXBLOCK0
$$

Answer:

The quadratic regression equation is \(f(x)=-15x^{2}+80x + 0\). The estimated height after \(0.25\) seconds is \(19\) feet.