Question

find the quadratic model of the data set provided. round to the nearest hundredth.
model ( f ( x ) = )

Explanation:

Step1: Input data into regression calculator

Let \(x\) be the temperature and \(y\) be the number surviving. Input the pairs \((20,40),(22,52),(24,64),(26,68),(28,64),(29,62),(30,61.3)\) into a quadratic regression calculator.

Step2: Get quadratic regression coefficients

A quadratic model is \(y = ax^{2}+bx + c\). Using a calculator (such as TI - 84 Plus: STAT → EDIT (input data), then STAT → CALC → QuadReg), we find \(a=-1.09\), \(b = 51.91\), \(c=-477.33\)

Answer:

\(f(x)=-1.09x^{2}+51.91x - 477.33\)