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Chapter 5 Section 3 Transforming Parabolas Algebra 2 Notes March 4, 2009 Warm-Ups • A rock club’s profits from booking local bands depends on the ticket price. Using past receipts, the owners find that the profit can be modeled by the function 1) What do t and P represent? 2) What is the maximum profit? 3) How much does the club have to sell the tickets for in order to achieve the maximum profit? Homework #33 Answers 8 22) 2 25) 6 4 -2 -4 Max Value = 6 28) $10; $13,500 29) 2 s; 64 ft 30) 1000 tires; $20 2 -5 -2 Min Value = 2 37) B 38) C 39) A Challenge Problem • The local park has 350 feet of fencing for a rectangular dog park. What dimensions maximize the area the dogs can play in? What is that area? 1. Write an expression for the perimeter in terms of x (width) and y (length) 2. Write an expression for the area of the rectangle in terms of x and y. 3. Solve your perimeter equation for y. Plug that into the area equation and simplify. 4. Use this equation to find the dimensions (x and y) that maximize the area. 5. Find the maximum area using these dimensions f ( x) x The “Parent” Function of the Quadratic: 2 5 We can transform the quadratic the same way we did with the absolute value function. 4 3 2 1 “VERTEX FORM”: f(x) = a(x –h)2 + k -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 -3 a, h, and k do the same things as before -4 -5 Notice how the graph increases. Up 1 over 1. Up 3 over 1. Up 5 over 1. Describe, in order, the sequence of transformations of each function and then graph the function by hand. 2 1) f ( x) 2 x 4 2) f ( x) 1 x 2 2 5 3) f ( x) 1 x 12 2 3 2 5 5 5 4 4 4 3 3 3 2 2 2 1 1 1 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 2 3 4 5 -5 -4 -3 -2 -1 1 -1 -1 -1 -2 -2 -2 -3 -3 -3 -4 -4 -4 -5 -5 -5 2 3 4 5 Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 3. Find a value for a: 2 -8 -6 -4 -2 2 -2 -4 -6 -8 4 6 8 Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 3. Find a value for a: 2 -8 -6 -4 -2 2 -2 -4 -6 -8 4 6 8 Write a function for the graph below. 1. How is the graph translated? __________________ 8 6 4 2. Use the translation to write an equation: __________________ 3. Find a value for a: 2 -8 -6 -4 -2 2 -2 -4 -6 -8 4 6 8 Homework #34 • Page 255 #1, 4, 9, 14, 16, 19, 25-27, 34, 42bcd, 47, 51 – Read Example 4 on page 255 to help you with #27 and #34 – Remember: Tutoring M-Th in the Media Center from 3:30-5:00 • 5 pts EC for every hour you go!!! • Bring me a sheet signed by Mr. Sloop with the date and the amount of time you were there!