1. WARM-UP: DISCUSS WITH YOUR PARTNER 1 Consider the function y = 3x 2 – 6x + 2. a)Does the graph open up or down? b)Find the line of symmetry of the graph of the function. c)Find the vertex of the graph of the function. d)Find the y -intercept. Opens Up x = 1 (1, -1) y = 2

2. 2 Graphing Quadratic Functions Algebra Unit 11

3. STEPS To graph a quadratic function perform the following steps: STEP 1: Put equation in standard form y = ax 2 + bx + c. STEP 2: Find the line of symmetry using and graph it. STEP 3: Find the vertex and plot it. STEP 4: Find two other points using a table. Use the next two numbers after the line of symmetry for the table. Reflect points across the line of symmetry. Connect the five points with a smooth curve. 3

4. 4 STEP 1: Put equation in standard form y = ax 2 + bx + c. STEP 2: Find the line of symmetry and graph it. MODELING Graph y = 2x 2 – 4x – 1. Already in standard form. Thus the line of symmetry is x = 1.

5. 5 STEP 3: Find the vertex and plot it. MODELING Graph y = 2x 2 – 4x – 1. Plug in x = 1 to find the y – value of the vertex. Thus the vertex is (1,–3).

6. 6 STEP 4: Find two other points using a table. MODELING Graph y = 2x 2 – 4x – 1. (1,–3) 3 2 yx –1 5 Reflect points across the line of symmetry. Use the next two numbers after the line of symmetry for the table. Connect the five points with a smooth curve. (2,–1) (3,5) (0,–1) (–1,5)

7. 7 STEP 1: Put equation in standard form y = ax 2 + bx + c. STEP 2: Find the line of symmetry and graph it. Graph y = – 2x 2 – 8x + 1. Already in standard form. Thus the line of symmetry is x = – 2. STRUCTURED PRACTICE

8. 8 STEP 3: Find the vertex and plot it. Graph y = – 2x 2 – 8x + 1. Plug in x = – 2 to find the y – value of the vertex. Thus the vertex is (–2, 9). STRUCTURED PRACTICE

9. 9 STEP 4: Find two other points using a table. Graph y = – 2x 2 – 8x + 1. (–4,1) 0 –1 yx 7 1 Reflect points across the line of symmetry. Use the next two numbers after the line of symmetry for the table. Connect the five points with a smooth curve. (–3,7)(–1,7) (0,1) (–2,9) STRUCTURED PRACTICE

10. INDEPENDENT PRACTICE 10 Begin Homework: page 522 #’s 45 - 50