Activating Strategy

1. Activating Strategy Sitback, watch, and be amazed! Then write down two things you learned from the video.

2. Topic 1: Graphing Quadratic Functions Algebra II: Unit 2 How are quadratic functions graphed? Book: 5.1

3. VOCAB • Quadratic Function • A function with a degree of 2 (highest exponent is 2) • Parabola • The shape of a quadratic functions graph • U-Shaped

4. VOCAB • Vertex • The lowest or highest point on the graph • Min (opens up) or Max (opens down) • Axis of Symmetry • The vertical line passing through the vertex Maximum Vertex Minimum

5. y = x2

6. Investigation on Graphing Calculator (y = ax2 + bx + c) If a > 1, graph gets narrower If 0 < a < 1, graph gets wider If a is positive, graph opens up If a is negative, graph opens down y = x2 y = 4x2 y = 1/4x2 y = -x2 y = -4x2 y = -1/4x2

7. Finding the Vertex • Formula • Axis of Symmetry

8. EXAMPLE • Find the vertex point and axis of symmetry. • y = 2x2 – 12x + 19 (3, 1) X = 3

9. YOUR TURN… • Find the vertex and axis of symmetry. • y = -x2 + 4x – 2 • y = -1/6x2 - x - 3 (2, 2) X = 2 (-3, -1.5) X = -3

10. Graphing a Quadratic in Standard Form 1) Identify a, b, and c 2) Calculate and plot the vertex 3) Draw the axis of symmetry 4) Find 2 more points…use symmetry 5) Connect to form a parabola

11. Example: y = 2x2 - 8x + 6 (2, -2)

12. Your Turn: y = x2 – 6x + 11

13. Your Turn: y = ½x2 - x - 6

14. Your Turn: y = -x2 + 2x + 8

15. Summarizing Strategy Describe how you know whether the graph of a parabola will open up or down. Be specific!

16. PRACTICE 5.1 Practice WS #1-10, 14

17. Activating Strategy y = -x2 + 2x - 4 Calculate the vertex.Does the graph open up/down? Why?Is the graph wider/narrower? Why?Does the graph have a min/max? Why?

18. Topic 1: Graphing Quadratic Functions Algebra II: Unit 2 How are quadratic functions graphed? Book: 5.1

19. Vertex Form y = a(x – h)2 + k

20. Investigation on Graphing Calculator (y = a(x – h)2 + k) If a is positive, graph opens up If a is negative, graph opens down If a > 1, graph gets narrower If 0 < a < 1, graph gets wider Vertex is given in equation @ (h, k) y = (x - 2)2+ 1 y = -(x + 1)2 - 3 y = 2(x – 5)2 + 2

21. Vertex?Open up/down?Wider/Narrower?Min/Max? y = -3(x – 2)2 + 1

22. Graphing a Quadratic in Vertex Form • Find and plot the vertex from original equation • Draw the axis of symmetry • Find 2 more points…use symmetry

23. Example: y = -(x – 2)2 - 1

24. Your Turn: y = 2(x +1)2 + 5

25. Your Turn: y = (x - 3)2

26. Intercept Form y = a(x – p)(x – q)

27. Investigation on Graphing Calculator (y = a(x – p)(x – q)) If a is positive, graph opens up If a is negative, graph opens down If a > 1, graph gets narrower If 0 < a < 1, graph gets wider X-intercepts are @ x = p and x = q y = (x - 2)(x + 1) y = -(x + 4)(x + 3) y = 2(x – 5)(x + 5)

28. Intercepts?Open up/down?Wider/Narrower?Min/Max? y = 3(x – 3)(x + 1)

29. Graphing a Quadratic in Intercept Form • Find and plot the intercepts from original equation • Draw the axis of symmetry (1/2 way between intercepts) • Calculate vertex from axis is symmetry. • Find 2 more points…use symmetry

30. Example: y = (x – 1)(x + 3)

31. Your Turn: y = -2(x + 2)(x – 2)

32. Your Turn: y = 1/2(x + 5)(x + 1)

33. Converting to Standard Form • Vertex to Standard • Rewrite and FOIL • Intercept to Standard • FOIL

34. Example Vertex to Standard • y = 2(x – 2)2 + 1 Intercept to Standard • y = (x – 2)(x – 7)

35. Your Turn… Vertex to Standard • y = -(x + 3)2 - 4 Intercept to Standard • y = 2(x – 1)(x + 5)

36. Application • The height, y, of an object, x seconds after it was thrown into the air is approximated by the quadratic function: y = -16x2 + 65x + 4 • Does this quadratic function have a maximum or minimum point? • Find it. • What does it tell us about the object?

37. Summarizing Strategy Describe how you can identify that the graph of an equation should form a parabola.

38. PRACTICE 5.1 Practice WS #16-21, 24, 26 - 32