1. Vertex Form November 10, 2014 Page 34-35 in Notes

2. Objective relate representations of quadratic functions, such as algebraic, tabular, graphical, and verbal descriptions[6.B]

3. Essential Question What parts of a quadratic function can I determine from the vertex form?

4. Vocabulary parabola: the shape of a quadratic function vertex: the highest or lowest point on a parabola y-intercept: the point where the graph crosses the y-axis x-intercepts: the points where the graph crosses the x-axis axis of symmetry: the vertical line that divides a parabola in two equal parts

5. Vertex Form f(x) = a(x – h) 2 + k – “a” reflection across the x-axis and/or vertical stretch or compression – “h” horizontal translation – “k”: vertical translation

6. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k h k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

7. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

8. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

9. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) Axis of symmetry: x = h y-intercept: (0, y)

10. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h y-intercept: (0, y)

11. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y)

12. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

13. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

14. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

15. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

16. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2 y-intercept: (0, y) (0, 4)

17. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)

18. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

19. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

20. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k0 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

21. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

22. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3 y-intercept: (0, y) (0, 4)(0, 8)

23. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)

24. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

25. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

26. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k04 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

27. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

28. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

29. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2x = -3 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)

30. What can we determine from the Vertex Form? Vertex Form: y=a(x-h) 2 + k y=(x–2) 2 y = (x+3) 2 – 1y= -3(x+2) 2 +4y= 2(x+3) 2 +1 h2-3-2-3 k041 Vertex: (h, k) (2, 0)(-3, -1)(-2, 4)(-3, 1) Axis of symmetry: x = h x = 2x = -3x = -2x = -3 y-intercept: (0, y) (0, 4)(0, 8)(0, -8)(0, 19)

31. To Graph from Vertex Form: 1.Identify the vertex and axis of symmetry and graph. 2.Find the y-intercept and graph along with its reflection. 3.Make a table (with the vertex in the middle) to calculate at least 5 points on the parabola.

32. Example 1 (Left Side): y = (x + 3) 2 - 1 h:_______ k:_______ vertex:__________ axis of symmetry: ___________ y-int: ________ xy -3(-3, -1) x = -3 y = (x + 3) 2 – 1 y = (0 + 3) 2 – 1 y = (3) 2 – 1 y = 9 – 1 y = 8 (0, 8) -3 -1 -4 0 -5 3 -2 0 -1 3

33. y = -3(x – 2) 2 + 4 y = -3(0 – 2) 2 + 4 y = -3(-2) 2 + 4 y = -3 4 + 4 y = -8 Example 2 (Left Side): y = -3(x – 2) 2 + 4 h:_______ k:_______ vertex:__________ axis of symmetry: ___________ y-int: ________ 24(2, 4) x = 2(0, -8) 2 4 1 1 0 -8 3 1 4 -8 xy

34. Assignment 1.f(x) = x 2 – 2 2.g(x) = -(x – 4) 2 3.h(x) = (x + 1) 2 – 3 4.j(x) = (x + 2) 2 + 2

36. Reflection 1.How do you know if a parabola will open upward or downward? 2.When does the parabola have a maximum point? 3.When does the parabola have a minimum point?