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Quadratic Functions as Mathematical Models (5.7)

Quadratic Functions as Mathematical Models (5.7). (a.k.a.: Word Problems) Aack, gaack, choke. Let’s see if we can make this process easy. The Method for Parabolas: 1. Read the problem carefully. 2. Identify the variables and their UNITS.

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Quadratic Functions as Mathematical Models (5.7)

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  1. Quadratic Functions as Mathematical Models (5.7) (a.k.a.: Word Problems) Aack, gaack, choke

  2. Let’s see if we can make this process easy. The Method for Parabolas: 1. Read the problem carefully. 2. Identify the variables and their UNITS. 3. Decide which variable is independent and which is dependent. 4. How many points do you need to determine a parabola? Find them. 5. Determine an equation for the quadratic model using your points-- remember, a system of equations in 3 variables. 6. Use that equation to answer the questions. Often this means to predict other points. Include UNITS in your answers!

  3. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. a. Write an equation for the amount charged as a function of the diameter of the pizza sold.

  4. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. a. Write an equation for the amount charged as a function of the diameter of the pizza sold. y = .1x2 - .3x + 4.5 You can confirm this with a quadratic regression.

  5. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. b. Why is this not a linear function? What does the y-intercept represent? c. Predict the price of a 20” pizza. d. What size pizza would you buy for $6.00?

  6. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. b. Why is this not a linear function? What does the y-intercept represent? The slopes between the points are different, so the points can’t lie on the same line. The y-intercept is the cost of 0 pizzas = overhead. c. Predict the price of a 20” pizza. $38.50 d. What size pizza would you buy for $6.00? About 5.7 inches

  7. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. e. What is the minimum cost for a pizza? (What point would this be?) f. Will the cost of the pizza ever be free? How do we know?

  8. Try it ’s Pizza Palace This place charges 8.50 for an 8” diameter pizza, $11.50 for a 10” pizza, and $17.50 for a 13” pizza. e. What is the minimum cost for a pizza? (What point would this be?) The vertex is (1.5, 4.28). The smallest pizza for this model would be 1.5” in diameter, and it would cost $4.28. But wait, how does this compare to our overhead? What does that mean about our model? f. Will the cost of the pizza ever be free? How do we know? Nope. The vertex is above the x-axis– there are no x-intercepts– y never equals 0.

  9. Try it You’ll do some of these in homework, of course. For the test, we’ll do something a little different. Instead of having word problems on a test per se, I’m asking you to do some research. As a part of the test, you are going to find a situation that can be modeled by a parabola. You’ll find data, determine the parabola, and then answer a few questions. I’ll give you a handout that explains it more fully, and the project will be due Thursday, Nov. 19th, the class after you take your test. Be sure to do all the parts!

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