Question

the average number of cars entering a shopping center parking lot is collected and shown in the table below.
find the quadratic model of the data set provided. round to the nearest thousandth.
model: y = - 0.014
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Explanation:

Step1: Use quadratic regression formula

Let \(x\) be the time (seconds) and \(y\) be the number of cars. Using a calculator or software for quadratic regression \(y = ax^{2}+bx + c\).

Step2: Input data points

Input the pairs \((20,70),(60,178),(100,260),(140,301),(180,284),(220,260),(240,195)\) into the regression tool.

Step3: Calculate coefficients

After calculation, \(a=- 0.014\), \(b = 3.371\), \(c=- 10.071\)

Answer:

\(y=-0.014x^{2}+3.371x - 10.071\)