Question

the table below shows the height of a ball x seconds after being kicked. 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: Input data into calculator

Use a graphing calculator or statistical software to perform quadratic regression on the data \((x = 0,y = 0)\), \((x=0.5,y = 35)\), \((x = 1,y=65)\), \((x=1.5,y = 85)\), \((x = 2,y=95)\), \((x=2.5,y = 100)\), \((x = 3,y=95)\).

Step2: Get quadratic regression coefficients

The quadratic regression formula is \(y=ax^{2}+bx + c\). After performing the regression (using the "QuadReg" function on a TI - 84 Plus calculator for example), we get \(a=-14\), \(b = 74\), \(c = 0\). So \(f(x)=-14x^{2}+74x+0\).

Step3: Calculate the height at \(x = 0.25\)

Substitute \(x = 0.25\) into \(f(x)=-14x^{2}+74x\).

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Answer:

The quadratic regression equation is \(f(x)=-14x^{2}+74x + 0\). The estimated height after \(0.25\) seconds is \(18\) feet.