quadratic functions
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This document discusses quadratic functions and how they can be used to model real-world situations. It provides an example of using a quadratic function to model how cutting a pizza into pieces relates to the number of cuts. The document also asks questions about recognizing patterns in tables of quadratic functions and using them to find values and make predictions. It explains that quadratic functions are useful for estimating one variable from another and making predictions about their relationship in different situations.
quadratic functions
- 4. Reasoning tells us that 3 straight cuts would result to 6 pieces and 5 straight cuts to 10 pieces. In other words, pizza-cutting this way can be described by the linear function where is the number of straight cuts and , the number of pieces that result. The corresponding table is shown below
- 5. Suppose what we want is the greatest number of pieces for the number of straight cuts we make. Drawing diagrams to find out, the results are shown below.
- 6. You will observe that the corresponding table of values will differ from that of the equation
- 7. Use the table to get the greatest number of pieces for 6 straight cuts.
- 8. Make a guess of the relation between the variables. Observation of the entries in the table should have led you to see the following relations:
- 9. Using for the number of straight cuts and for the maximum number of pieces, we get
- 10. Does each table show a pattern? Explain your answer?
- 11. a. Is quadratic function useful in real-life situations?
- 12. b. How can quadratic function be used to solve real-life problems?
- 13. There are many situations in the real world that can be modeled or mathematically described by the quadratic function. Skill to do this can be useful to make estimates of one variable from known values of the related variable or to make predictions of the relationship between the same two variables in a different situation.
- 14. Directions: Use values of x and y to complete the table below: x 2 4 6 8 10 12 14 y 4 8 12 20
- 15. x 2 4 6 8 10 12 14 y 4 8 12 16 20 24 28
- 16. Directions: Use the table below to determine the greatest number of pieces for 6 straight cuts. x 0 1 2 3 4 5 6 y 1 2 4 7
- 17. x 0 1 2 3 4 5 6 y 1 2 4 7 11 16 22
- 18. Menggay maintains a small retail store to help support her family. Think of the diagram below as rows of bath soap.
- 20. b. Do you see a pattern in the entries in the table? c. Extend the table to rows 5, 6 and 7. What will be the corresponding values for ? d. Make a guess of the equation of the function.
- 22. A quadratic function is defined by the general equation 𝑦 = 𝑥2 + 𝑏𝑥 + 𝑐 where 𝑎 𝑏 and 𝑐 are real numbers and 𝑎 ≠ 0
- 23. VS.