MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a...

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MAT 150 – Algebra Class #11 Topics: • Find the exact quadratic function that fits three points on a parabola • Model data approximately using quadratic functions

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Transcript of MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a...

Page 1: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

MAT 150 – AlgebraClass #11Topics:

• Find the exact quadratic function that fits three points on a parabola

• Model data approximately using quadratic functions

Page 2: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Speed vs. Fuel EconomyA study compared the speed x (in miles per hour) and the average fuel economy y (in miles per gallon) for cars. The results are shown in the table. Using the function, what is the fuel economy if the speed is 47?

Speed, x Fuel Economy, y

15 22.3

20 25.5

25 27.5

30 29

35 28.8

40 30

45 29.9

50 30.2

55 30.4

60 28.8

65 27.4

70 25.3(Source: Transportation Energy Data Book)

Page 3: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Writing a Quadratic Function

• A parabola passes through the points (0, 5), (4, 13) and (-2, 25). Write the equation of the quadratic function whose graph is this parabola.

Page 4: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Speed vs. Fuel EconomyA study compared the speed x (in miles per hour) and the average fuel economy y (in miles per gallon) for cars. The results are shown in the table. Using the function, what is the fuel economy if the speed is 47?

• Plot the data points. Is it linear or quadratic?

• Write the equation of this function.

Speed, x Fuel Economy, y

15 22.3

20 25.5

25 27.5

30 29

35 28.8

40 30

45 29.9

50 30.2

55 30.4

60 28.8

65 27.4

70 25.3(Source: Transportation Energy Data Book)

Page 5: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Quadratic Regression

Using the pervious data, put the data into your calculator where Speed is List 1 and Fuel Economy is List 2

Now select STAT, CALC, 5: QuadReg

What is the fuel economy if the speed is 47?

When can we be certain that this model no longer applies?

Page 6: MAT 150 – Algebra Class #11 Topics: Find the exact quadratic function that fits three points on a parabola Model data approximately using quadratic functions.

Assignment

Pg. 223-230

#1 , 5 and 8

#12 & 15

#29 & 35


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