October 10, 2012

1. October 10, 2012 • Take out your graphing calculator. • If at least 70% of students in the class have their graphing calculator in class today, we will do an activity with the calculator. • If not, we will take notes on 5.2.

2. Homework Questions?

3. PSAT Questions?

4. Graphing on TI-83/TI-84

5. Graph using your calculator • Graph each of the following using your graphing calculator, and sketch the graph on your paper.

6. Warm-Up: Find the vertex, roots, and y-intercept of f(x) = x2 + 4x – 5

7. Due: Page 311 #11-27 odd

8. Graphing Parabolas

9. Purpose • Learn how to graph parabolas

10. Outcome • Graph parabolas

11. Graphing Parabolas, Method 1 • Solve for the following: • Axis of symmetry • Vertex • y-intercept (c) • x-intercepts (also called the zeros or the roots) • Draw a dashed line for the axis of symmetry • Draw a point for: • The vertex • The y-intercept • The reflection of the y-intercept • The x-intercepts • Sketch in the rest of the parabola • Check that the shape agrees with the shape predicted by the sign of a • a>0 (a is positive) opens up • a<0 (a is negative) opens down

12. Example 1: Graph (-2) Vertex = (-2, -1) y-intercept = 3  (0, 3) Reflection of y-intercept (-4, 3) Solve for the roots/zeros/x-intercepts

13. You-Try: Graph f(x) = 6 + x – x2 Axis of symmetry: Vertex (from Warm-Up) = (.5, 6.25) y-intercept = 6  (0, 6) Reflection of y-intercept = (1, 6) Solve for the roots/zeros/x-intercepts (from Warm-Up) (-2, 0), (3, 0)

14. Graphing Parabolas, Method 2 • Solve for the following: • Axis of symmetry • Vertex • y-intercept (c) • Draw a dashed line for the axis of symmetry • Draw a point for: • The vertex • The y-intercept • The x-intercepts • The points with x-values ±1 and ±2 of the vertex • Sketch in the rest of the parabola • Check that the shape agrees with the shape predicted by the sign of a • a>0 (a is positive) opens up • a<0 (a is negative) opens down

15. Vertex Form • If has its vertex at (h, k), then it can be written in vertex form as • This is similar to shifting absolute value equations.

16. Example 3 • Given the graph of y = x2, graph the following: • y = (x-3)2 + 5 • y = (x+1)2 + 3 • y = (x+4)2 – 7

17. Assignment • Parabola Graphing Worksheet

19. Alternate Lesson

20. Warm-Up: October 23, 2012 • Solve by factoring:

21. Homework Questions?

22. Graphing Parabolas

23. Essential Question • How can we graph quadratic functions?

24. Vertex • The vertex is the minimum or maximum point of a parabola. • The x-coordinate of the vertex is • To find the y-coordinate, substitute the x value into the original equation. • The vertex is a point, expressed as an ordered pair.

25. Graphing Parabolas • Find the vertex. • Plot the vertex and draw a vertical dashed line to represent the axis of symmetry. • Set up a T-table with the vertex in the middle. • Choose 3 x-values on each side of the vertex. • Find each y-value by substituting the x-value into the original equation. • Plot your points. • Connect the points with a smooth curve.

26. Example 1: Graph

27. You-Try #1: Graph

28. Vertex Form • If has its vertex at (h, k), then it can be written in vertex form as • The graph will look like y=x2, but shifted to the right h units and shifted up k units.

29. Example 3 • Given the graph of y = x2, graph the following: • y = (x-3)2 + 5 • y = (x+1)2 + 3 • y = (x+4)2 – 7

30. Assignment • Parabola Graphing Worksheet