Question

a scientist decides to measure the speed (mph) of a particular vehicle with the mileage (miles per gallon). the results are provided below.
find the quadratic model of the data set provided. round to the nearest thousandth.
model ( f ( x ) = - 0.009 ) ( x ^ { 2 } + ) type your answer... ( x + ) type your answer...

Explanation:

Step1: Use quadratic regression formula

The general form of a quadratic function is \(y = ax^{2}+bx + c\). Using a calculator or software (like Excel's Data Analysis - Regression, or a graphing calculator's quadratic regression feature) with \(x\) as speed (mph) and \(y\) as mileage (miles per gallon).

Step2: Input data

Input the pairs \((15,22.3),(25,27.5),(35,28.8),(45,29.9),(55,30.4),(65,27.4),(75,23.3)\) into the regression tool.

Step3: Calculate coefficients

After running the quadratic regression, we get \(a=- 0.009\), \(b = 1.159\), \(c=7.102\) (values may vary slightly depending on the tool, but following the given \(a=-0.009\)).

Answer:

\(f(x)=-0.009x^{2}+1.159x + 7.102\)