1. 1 Properties of Quadratic Function Graphs Algebra Unit 11

2. WARM-UP: DISCUSS WITH YOUR PARTNER 2 1. Find the y-intercept: a. b. 2. Simplify: a. b. 3. Add: Let x=0 y-int (0,-7) y-int (0,6)

3. y = ax 2 + bx + c The parabola will open down when the a value is negative. The parabola will open up when the a value is positive. The standard form of a quadratic function is a > 0 a < 0 The graph of a quadratic function is called a parabola.

4. VERTEX THE VERTEX IS THE HIGHEST OR LOWEST POINT OF THE PARABOLA. Vertex

5. y x Line of Symmetry LINE OF SYMMETRY Parabolas have a symmetric property to them. line of symmetry– the line that goes thru the vertex and divides the parabola in half.

6. FINDING THE LINE OF SYMMETRY The equation of the line of symmetry is

7. FINDING THE VERTEX STEP 1: Find the line of symmetry STEP 2: Plug the x – value into the original equation to find the y value. STEP 3: Write the answer as a coordinate.

8. FINDING THE Y-INTERCEPT Step 1: Let x = 0 Step 2: Simplify, write the answer as a coordinate. This means that the y-intercept of a quadratic function is always the value of c.

9. MODELING 9

10. EXAMPLE #1 10 Consider the function y = – 2x 2 + 12x – 7. b. Find the line of symmetry of the graph of the function. c. Find the vertex of the graph of the function. a. Does the graph open up or down? d. Find the y-intercept.

11. EXAMPLE #1 11 Consider the function y = – 2x 2 + 12x – 7. a. Does the graph open up or down? b. Find the line of symmetry of the graph of the function.

12. EXAMPLE #1 CONTINUED 12 Consider the function y = – 2x 2 + 12x – 7. c. Find the vertex of the graph of the function. Step 1 Find the line of symmetry Step 2 Plug the x – value into the original equation to find the y value. Step 3 Write the answer as a coordinate. Step 1 Step 2 Step 3

13. EXAMPLE #1 CONTINUED 13 Consider the function y = – 2x 2 + 12x – 7. y-intercept is (0, c) d. Find the y-intercept.

14. STRUCTURED PRACTICE 14

15. STRUCTURED PRACTICE #1 15 Consider the function y = 4x 2 – 4x + 8. b. Find the line of symmetry of the graph of the function. c. Find the vertex of the graph of the function. a. Does the graph open up or down? d. Find the y-intercept.

16. STRUCTURED PRACTICE #1 16 Consider the function y = 4x 2 – 4x + 8. a. Does the graph open up or down? b. Find the line of symmetry of the graph of the function.

17. STRUCTURED PRACTICE #1CONTINUED 17 Consider the function y = 4x 2 – 4x + 8. c. Find the vertex of the graph of the function. Step 1 Find the line of symmetry Step 2 Plug the x – value into the original equation to find the y value. Step 3 Write the answer as a coordinate. Step 1 Step 2 Step 3

18. STRUCTURED PRACTICE #1 CONTINUED 18 Consider the function y = 4x 2 – 4x + 8. y-intercept is (0, c) d. Find the y-intercept.

19. GUIDED PRACTICE 19 Do problems on your own Label the steps Then compare answers with your partner

20. GUIDED PRACTICE #1 20 Consider the function y = – 6x 2 – 2x + 4. b. Find the line of symmetry of the graph of the function. c. Find the vertex of the graph of the function. a. Does the graph open up or down? d. Find the y-intercept.

21. GUIDED PRACTICE #1 21 Consider the function y = – 6x 2 – 2x + 4. a. Does the graph open up or down? b. Find the line of symmetry of the graph of the function.

22. GUIDED PRACTICE #1CONTINUED 22 Consider the function y = – 6x 2 – 2x + 4. c. Find the vertex of the graph of the function. Step 1 Find the line of symmetry Step 2 Plug the x – value into the original equation to find the y value. Step 3 Write the answer as a coordinate. Step 1 Step 2 Step 3

23. GUIDED PRACTICE #1 CONTINUED 23 Consider the function y = – 6x 2 – 2x + 4. y-intercept is (0, c) d. Find the y-intercept.

24. GUIDED PRACTICE #2 24 Consider the function y = 5x 2 – x. b. Find the line of symmetry of the graph of the function. c. Find the vertex of the graph of the function. a. Does the graph open up or down? d. Find the y-intercept.

25. GUIDED PRACTICE #2 25 Consider the function y = 5x 2 – x. a. Does the graph open up or down? b. Find the line of symmetry of the graph of the function.

26. GUIDED PRACTICE #2CONTINUED 26 Consider the function y = 5x 2 – x. c. Find the vertex of the graph of the function. Step 1 Find the line of symmetry Step 2 Plug the x – value into the original equation to find the y value. Step 3 Write the answer as a coordinate. Step 1 Step 2 Step 3

27. GUIDED PRACTICE #2 CONTINUED 27 Consider the function y = 5x 2 – x. y-intercept is (0, c) d. Find the y-intercept.

28. INDEPENDENT PRACTICE 28 Complete the classwork and turn it in before you leave