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