Name ——————————————————————— Date ———————————— Practice A LESSON 1.2 For use with the lesson “Graph Quadratic Functions in Vertex or Intercept Form” Match the equation with its graph. 1. y 5 (x 2 1) 2 2. y 5 (x 2 2)(x 1 4) 3. y 5 22(x 1 1) 2 1 3 A. B. C. y y y 2 4 1 x 1 1 1 x x Graph the function. Label the vertex and axis of symmetry. 4. y 5 (x 2 1) 2 1 1 5. y 5 (x 2 3) 2 1 2 y 6. y 5 (x 1 1) 2 2 2 y y 1 1 1 x 7. y 5 2(x 1 1) 2 1 2 1 x 8. y 5 4(x 2 2) 2 2 1 y LESSON 1.2 x 1 9. y 5 22(x 2 3) 2 2 3 y y 1 x 21 1 1 1 1 x x Graph the function. Label the vertex, axis of symmetry, and x-intercepts. 10. y 5 (x 2 1)(x 2 5) 11. y 5 (x 1 2)(x 2 2) y y 1 y 1 1 1-22 12. y 5 (x 1 6)(x 1 2) Algebra 2 Chapter Resource Book x 1 1 x 21 x Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 1 Name ——————————————————————— LESSON 1.2 Date ———————————— Practice A continued For use with the lesson “Graph Quadratic Functions in Vertex or Intercept Form” 13. y 5 2(x 1 3)(x 2 1) 14. y 5 2(x 1 1)(x 2 2) y 15. y 5 23(x 2 1)(x 1 4) y y 1 1 x 1 1 x 3 3 x Write the quadratic function in standard form. 16. y 5 2(x 2 1) 2 1 1 17. y 5 2(x 1 3) 2 1 5 18. y 5 3(x 2 2) 2 2 7 19. y 5 (x 2 3)(x 2 1) 20. y 5 2(x 1 1)(x 1 4) 21. y 5 23(x 2 2)(x 1 3) 22. y 5 (x 2 3) 2 1 1 23. y 5 22(x 1 1) 2 1 5 24. y 5 4(x 2 2) 2 2 7 25. y 5 (x 1 3)(x 1 1) 26. y 5 2(x 2 1)(x 2 5) 27. y 5 24(x 2 3)(x 1 2) In Exercises 28 and 29, use the following information. Height (yards) Golf The flight of a particular golf shot can be modeled by the function y 5 20.0015x(x 2 280) where x is the horizontal distance (in yards) from the impact point and y is the height (in yards). The graph is shown below. LESSON 1.2 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. Find the minimum value or the maximum value of the function. y 35 30 25 20 15 10 5 0 x 0 80 160 240 Horizantal distance (yards) 28. How many yards away from the impact point does the golf ball land? 29. What is the maximum height in yards of the golf shot? Algebra 2 Chapter Resource Book 1-23 1 1 73 c. 24x 2 1 5 0; 2}, } 4 8 Lesson 1.1 Graph Quadratic Functions in Standard Form, continued 7. Model A is preferable because profits are positive and increasing. Lesson 1.2 Graph Quadratic Functions in Vertex or Intercept Form Height (yards) 1. down 2. maximum value y 16 12 8 4 0 Teaching Guide ANSWERS Real-Life Application 3. 2 1. 0 4 8 12 16 20 24 28 32 36 40 x Length (yards) 5. Height (yards) 4. 15 yd y 16 12 8 4 0 The graph of y 5 3x2 1 5 is a vertical shift of the graph of y 5 3x2. 2. 0 4 8 12 16 20 24 28 32 x Length (yards) 6. about 19 yd 7. no Challenge Practice 1. 2. y The graph of y 5 3(x 2 1)2 is a horizontal shift of the graph of y 5 3x2. 3. The graph of y 5 x2 is shifted k units vertically. 4. The graph of y 5 x2 is shifted h units horizontally. y 2 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 2 x Investigating Algebra Activity 2 2 3 61 ; 2}2 1 2}23, } 42 35 425 35 , 2} ; 2} 1 2} 18 36 2 18 3. 1. The parent function y 5 x 2 is shifted to the x 4. y y 2 21 x 2 x 2 13 6 ;} 1 }65, 2} 20 2 5 15 377 15 ,} ;} 1} 2 24 2 2 2 5. The coefficient of the x -term of the quadratic function is half of the coefficient of the x-term of the linear equation. The coefficient of the x-term of the quadratic function is the same as the constant term of the linear equation. 1 1 2 2 50 6. a. 6x 2 4 5 0; }, } 3 3 51 1 b. 220x 1 5 5 0; }, 2} 8 4 right if a number is subtracted from x and to the left if a number is added to x before squaring. 2. The parent function y 5 x 2 is shifted down if a number is subtracted from x 2 and up if a number is added to x 2 after squaring. 3. The parent function y 5 x 2 would be shifted 4 units to the right and 5 units up. 4. The vertex form of a quadratic function makes it easy to see how the parent function y 5 x 2 has been translated. The value of h gives the horizontal shift and the value of k gives the vertical shift. Practice Level A 1. A 2. C 3. B 4. 5. y 1 2 (3, 2) 1 (1, 1) x51 y x 1 x x53 2 Algebra 2 Chapter Resource Book A3 Lesson 1.2 Graph Quadratic Functions in Vertex or Intercept Form, continued 6. 7. y 4. 1 1 x (2, 21) 1 1 x 5 21 1 y (21, 3) y x 5 21 (21, 2) 5. y x52 x 1 1 1 x x 6. 7. y y x 5 21 2 x 22 (21, 22) (21, 24) 1 x 5 21 1 x 8. 9. y x 5 22 x53 y 1 x 21 1 (3, 23) 1 x (22, 23) 8. 9. y (2, 21) x52 1 x x 5 22 2 23 11. y 1 y 1 (1, 0) (5, 0) 2 (22, 24) (2, 0) 1 x 10. 12. 1 (26, 0) 2 13. (21, 4) 1 x 5 22 12. y 13. y x51 (1, 4) 1 (23, 0) 15. y 1 (2, 0) 1 x 21 (24, 0) (23, 21) (22, 0) y 3 75 4 ( , ) 3 2 x 2 14. ( 1 , 2 9 22 ) (4, 0) y 2 1 (3, 0) x 2 16. y 5 2x 2 4x 1 3 17. y 5 2x 2 6x 2 4 18. y 5 3x 2 2 12x 1 5 19. y 5 x 2 2 4x 1 3 y (7, 0) ( , ) 7 2 147 4 (4, 0) x 22 2 15. 5 x 52 (1, 0) 3 (21, 0) x 5 23 1 3 x 22 x 52 7 x (1, 0) x 2 6 ( 5 , 2 2 ) 27 4 (0, 0) 3 x 20. y 5 2x 2 1 10x 1 8 16. y 5 x 2 2 4x 1 10 17. y 5 22x 2 2 4x 1 1 21. y 5 23x 2 2 3x 1 18 18. y 5 3x 2 2 18x 1 15 19. y 5 x 2 2 6x 1 8 22. minimum, 1 23. maximum, 5 20. y 5 4x 2 1 12x 1 8 24. minimum, 27 25. minimum, 21 21. y 5 23x 2 1 3x 1 18 26. minimum, 28 27. maximum, 25 22. minimum, 3 23. maximum, 24 28. 280 29. 29.4 24. minimum, 23 25. minimum, 24 Practice Level B 25 26. minimum, 22 27. maximum, } 4 1. C 2. B 3. A A4 1 x ) 1 2 4 (22, 0) x (24, 24) x 5 24 (21, 0) 5 , 2 5 (1, 0) 2 14. (2 (1, 29) x (22, 0) 1 (23, 0) x x51 y x 5 21 21 y (4, 0) 2 x50 y 11. y (22, 0) (0, 24) x53 x x (22, 0) (3, 24) 2 Algebra 2 Chapter Resource Book 28. As a increases, the graph becomes more narrow and the vertex moves down. 29. 260 30. 16.9 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 10. x54 (4, 8) y