the table shows the average weekly earnings of repair people based on the hourly rate they charge

Question

Hourly Rate ($)                   Weekly Earnings ($)

10                                                  700

25                                                 1450

45                                                 1890

65                                                 1690

90                                                  540

 

 

Question 1: Is there an hourly rate that will maximize the repair person's earnings? explain your answer.

Question 2: determine the equation for the parabola of best fit for the data. Round the numbers in your equation to one decimal place.

Question 3: what the coordinates for the vertex of your parabola in the best fit possible.

Question 4: what is the meaning of the vertex point?

Question 5: what hourly rate will allow the repair person to make the most money? (round to the nearest penny)

 

 

Answer 1

1.

 

1890 is the largest Weekly Earnings in the table, so ...

 

2.

 

f(x) = -0.8x^2 + 78x from GeoGebra's FitPoly[ points, 2 ]

 

Your graphing calculator can do the same.

 

3.

 

f(x) = (-0.8x + 78)x so Zeros are x = 0 and -0.8x + 78 = 0, or

x = 78/0.8 = 780/8 = 390/4 = 195/2

 

Axis of Symmetry half way between Zeros:

 

x = 195/4

 

So vertex at (195/4, f(195/4)) ...

 

4. & 5. are related. Your studies of Quadratic Equations should allow you to answer them.