1. Graphing Quadratic Equations a step-by-step guide with practice

2. Graphing from Standard Form Graph y = x 2 – 6x + 8. go to next slide for step 1

3. Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 1: Find the axis of symmetry. go to next slide for step 2

4. Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 2: Find the vertex. Vertex: (3, – 1) go to next slide for step 3

5. Graphing from Standard Form Graph y = x 2 – 6x + 8. Step 3: Complete an x/y table. xy 13 20 3-1 40 53 go to next slide for final graph

6. Graphing from Standard Form Graph y = x 2 – 6x + 8. What are the solutions? x = 2 and x = 4

7. Graphing from Standard Form Try this one: Graph y = – x 2 + 5x – 2.

8. Graphing from Standard Form Try this one: Graph y = – x 2 + 5x – 2.

9. Graphing from Intercept Form Graph y = (x – 4)(x + 2). go to next slide for step 1

10. Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 1: Find the x-intercepts. x – 4 = 0 x = 4 x + 2 = 0 x = – 2 go to next slide for step 2

11. Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 2: Find the axis of symmetry. go to next slide for step 3

12. Graphing from Intercept Form Graph y = (x – 4)(x + 2). Step 3: Complete an x/y table. xy -1-5 0-8 1-9 2-8 3-5 go to next slide for final graph

13. Graphing from Intercept Form Graph y = (x – 4)(x + 2). What are the solutions? x = – 2 and x = 4

14. Graphing from Intercept Form Try this one: Graph y = (x + 3)(x + 1).

15. Graphing from Intercept Form Try this one: Graph y = (x + 3)(x + 1). What are the solutions? x = – 3 and x = – 1

16. Graphing from Vertex Form Graph y = 2(x – 1) 2 + 3 go to next slide for step 1

17. Graphing from Vertex Form Graph y = 2(x – 1) 2 + 3 Step 1: Find the vertex. vertex: (1, 3) go to next slide for step 2

18. Graphing from Vertex Form Graph y = 2(x – 1) 2 + 3 Step 2: Find the axis of symmetry. go to next slide for step 3

19. Graphing from Vertex Form Graph y = 2(x – 1) 2 + 3 Step 3: Complete an x/y table. xy -111 05 13 25 311 go to next slide for final graph

20. Graphing from Vertex Form Graph y = 2(x – 1) 2 + 3 What are the solutions? There are NO real solutions … later we will learn how to find the imaginary/complex solutions!

21. Graphing from Vertex Form Try this one: Graph y = – (x + 1) 2 + 2

22. Graphing from Vertex Form Try this one: Graph y = – (x + 1) 2 + 2