Answer
A) $ -0.0430893x^{2}+4.19289x-56.19 $
B) See included Graph
C) 23.6968571429
D) 36.5571428571
Work Step by Step
A) First we need to load the values into a graphing utility with graphing functionality. We are given 6 data points to input:
$ (20,10) , (20,31.9) , (40,42.2) , (50,44.7) , (60,41.3) , (70,25.9) $
After imputing these values, we need to use the regression system of the graphing utility. The Question states that it is a quadratic function, thus we are fitting the function to the form of $ax^{2}+bx+c$. This process varies based on your graphing utility. But it will result in the same approximate answer of:
$ a = -0.0430893 , b = 4.19289 , c = -56.19 $
Pluging this back into our quadratic form we get:
$ -0.0430893x^{2}+4.19289x-56.19 $
B) This question requires a graph as an answer, simply put the expression from part A, $ -0.0430893x^{2}+4.19289x-56.19 $, into your graphing utility.
C) For this part of the question we use the equation from part A, but we substitute the values given for x.
$ -0.0430893(26)^{2}+4.19289(26)-56.19 $
This resolves to $23.6968571429$
C) For this part of the question we use the equation from part A, but we substitute the values given for x.
$ -0.0430893(34)^{2}+4.19289(34)-56.19 $
This resolves to $36.5571428571$
