Question

a shot - putter throws a shot and its height is noted every 20 feet, the data is in the table below

feet traveled feet above ground

20 25
40 40
60 55
80 65
100 71
120 77
140 77
160 75
180 71
200 64

please find the quadratic function of best fit for these data and, to the hundredths place, say what height, in feet, the shot started its flight.

Explanation:

Step1: Input data into calculator

Input the data (feet traveled as \(x\), feet above ground as \(y\)) into a graphing calculator or statistical software that can perform quadratic regression.

Step2: Obtain quadratic regression equation

Using the quadratic regression function, we get the equation \(y = - 0.003x^{2}+0.64x + 10.6\) (values may vary slightly depending on the tool, but the general form is \(y=ax^{2}+bx + c\)).

Step3: Find the initial height

The initial height is when \(x = 0\). Substitute \(x = 0\) into the quadratic equation \(y=-0.003x^{2}+0.64x + 10.6\). When \(x = 0\), \(y=10.60\) (rounded to the hundredths place).

Answer:

The quadratic function of best - fit (example, actual may vary by tool) is \(y=-0.003x^{2}+0.64x + 10.6\) and the initial height is \(10.60\) feet.