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SOLVING PROBLEMS INVOLVING POLYNOMIAL FUNCTIONS.pptx
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- 3. Describe the behaviorof the graph of each polynomial function through different dance moves. 1. 𝑃 𝑥 = 𝑥4 − 𝑥2 + 3𝑥 + 6
- 4. Describe the behaviorof the graph of each polynomial function through different dance moves. 2. 𝑃 𝑥 = −𝑥6 + 2𝑥3 − 5𝑥 + 1
- 5. Describe the behaviorof the graph of each polynomial function through different dance moves. 3. 𝑃 𝑥 = −𝑥3 − 4𝑥 + 2
- 6. Describe the behaviorof the graph of each polynomial function through different dance moves. 4. f 𝑥 = (𝑥 + 2)3 (𝑥 − 1)2
- 7. What do thesepictures tell us?
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- 9. LESSON OBJECTIVES: At theend of the lesson, you are expected to: 1. Evaluate polynomial functions. 2. Solve word problems involving polynomial functions. 3. Give the importance of polynomial functions in solving real-life problems.
- 10. THINK-PAIR-SHARE “Lightning andThunder” In thePhilippines, the Habagat (southwest monsoon) occurs in May-October. It’s the wet season and typhoon season. A thunderstorm is a storm with lightning and thunder. Thunder is the sound produced by lightning. Because light travels faster than sound, during a thunderstorm we see lightning before we hear thunder.The farther away the storm, the more time will be between seeing the lightning and hearing the thunder.
- 11. THINK-PAIR-SHARE The formula 𝑑𝑡 = 1 3 𝑡 describes approximately the distance, in kilometers, of the storm’s center if it takes t seconds to hear thunder after seeing lightning. 1.What kind of polynomial function is represented by 𝑑 𝑡 = 1 3 𝑡 ? 2. If there was 30 seconds between the time you saw the lightning and when you heard the thunder, approximately, how far away did the lightning strike? 10 s? 60 s?
- 12. 3. If alightning strike is 800 meters away, how many seconds would pass before you are able to hear it? 4. How did you get the answer in number 3? THINK-PAIR-SHARE
- 13. Problem #2 •Suppose thatthe cost C(x) in pesos of producing x shirts in a garments shop in Oton is given by 𝐶 𝑥 = 0.1𝑥2 + 8𝑥 + 400. How much is the production cost if 100 pieces of shirts are produced? How much is the production cost if 1,000 pieces of shirts are produced?
- 14. SOLUTION: • Let x= 100 𝐶 𝑥 = 0.1𝑥2 + 8𝑥 + 400 𝐶 100 = 0.1(100)2 +8(100) + 400 𝐶 100 = 0.1(10000) + 800 + 400 𝐶 100 = 1000 + 800 + 400 𝐶 100 = 2, 200 Thus, it will cost 2,200 pesos for producing 100 shirts.
- 15. SOLUTION: b. Let x= 1000 𝐶 𝑥 = 0.1𝑥2 + 8𝑥 + 400 𝐶 1000 = 0.1(1000)2 + 8(1000) + 400 𝐶 1000 = 0.1(1,000,000) + 8000 + 400 𝐶 1000 = 100,000 + 8000 + 400 𝐶 1000 = 108,400 Thus, the production cost will be 108,400 pesos for 1000 shirts.
- 17. Group 1 –Population Problem Group 2 – Distance Problem Group 3 – Geometry Problem Group 4 – Business Problem
- 18. GROUP ACTIVITY Group 1(Population Problem) A demographer in Bayan ng Oton predicts that the population, 𝑃, of a town, t years from now can be modeled by the function 𝑃 𝑡 = 6𝑡4 − 5𝑡3 + 200𝑡 + 12,000. What will the population of the town be two years from now?
- 19. GROUP ACTIVITY Group 2(Distance Problem) One sunny Sunday, your family decided to have a family road trip. It is given that the distance D travelled in kilometers can be determined by the function 𝐷 𝑡 = 3𝑡3 − 𝑡2 + 2𝑡 where t is the travel time in. How many kilometers did your family travel at 5 hours?
- 20. GROUP ACTIVITY Group 3(Geometry Problem) A farmer has a poultry farm whose area is expressed by the polynomial function 𝐴 𝑥 = 8𝑥2 + 90𝑥 + 12 square meters. What is the actual land area of the poultry farm if x=3 meters?
- 21. GROUP ACTIVITY Group 4(Business Problem) A car manufacturer determines that the company’s profit, P, can be modeled by the function 𝑃 𝑥 = 𝑥4 + 2𝑥 − 3, where x represents the number of cars sold. What is the profit when x=20?
- 22. Group 1 –Population Problem Group 2 – Distance Problem Group 3 – Geometry Problem Group 4 – Business Problem
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- 24. QUESTIONS: •How do youfeel about the task given to your group? Why? •In doing the activity, what mathematics concepts or principles did your group apply? Explain how you applied these mathematics concepts or principles.
- 25. Let’s ponder onthis…. •How is polynomial function applied to real life problems? •Is it important to you as a learner? In what particular way?
- 26. GENERALIZATION •Real-life problems canbe modeled with polynomial functions.
- 27. It’s test time! •Prepare1 whole sheet of paper
- 28. Directions: Read andanalyze each situation carefully. Answer the given problem as required. Show a step-by-step solution in answering the given problem. You may use a calculator if needed. 1. Annie went to the grocery and bought items which cost 𝐶 𝑥 = 5𝑥4 + 2𝑥3 + 4𝑥 + 18 𝑝𝑒𝑠𝑜𝑠. If x is 4.00 𝑝𝑒𝑠𝑜𝑠, how much did Annie pay? 2. The number of tourists who visited Oton NHS can be modeled by the function v(t)=2t4-10t3+2t+5 where v(t) is the number of visitors and t is the number of months. a. How many visitors visited Oton NHS on the 5th month? b. How many visitors visited Oton NHS on the 12th month?
- 29. The end…. Thank youso much!