1. 1.7 Graphing Quadratic Functions

2. 1. Find the x-intercept(s). The x-intercepts occur when Solve by: Factoring Completing the Square Quadratic Formula y = 0 We will get to this! Use substitution!!

3. 2. Find the y-intercept. The y-intercept occurs when When the function is in the form y = ax 2 + bx + c, x = 0 c is the y-intercept. Use substitution!!

4. 3. Find the axis of symmetry.

5. 4. Find the vertex.

6. 4. Finding the vertex y = ax 2 + bx + c

7. 4. Finding the vertex.

8. 4. Finding the vertex y = ax 2 + bx + c

9. Practice: Graph the following quadratic functions. 1. y = 2x 2 – 7x + 5 2. y = –2x 2 + 12x + 4

10. Factored Form What if we had a quadratic that is factored? Consider y = (2x-1)(x-3) What’s the vertex?

11. Factored Form Consider y = (2x-1)(x-3) What’s the vertex? Find the x-intercepts.

12. Factored Form Consider y = (2x-1)(x-3) What’s the vertex? Find the x-intercepts. Now average them! This is your x-value for your vertex. Find the y-value.

13. Predicting what the graph will look like… If a > 0, the graph opens upward If a < 0, the graph opens downward

14. Vertex Form of a Quadratic Function y = a(x – h) 2 + k The vertex is (h, k). a is just some constant Ex: y = 2(x – 3) 2 + 7 The vertex is (3, 7) Ex: y = –4(x + 9) 2 + 2 => y = –4(x – – 9) 2 + 2 The vertex is (–9, 2)

15. Graphing in Vertex Form Example: y = 3(x – 2) 2 – 9

16. 1. Find the vertex. y = 3(x – 2) 2 – 9 y = 3(x – 2) 2 + – 9 The vertex is (2, –9)

17. 2. Find the axis of symmetry. The axis of symmetry will always be the vertical line: x = (the x-coordinate of the vertex) For the function y = 3(x – 2) 2 – 9, the axis of symmetry is: x = 2

18. 3. Find the y-intercept. y = 3(x – 2) 2 – 9 The y-intercept happens when x = 0. y – intercept = 3

19. 4. Find the x-intercept.

20. Practice: Graph y = (x+2) 2 – 3

21. Practice: Graph y = (x+2) 2 – 3

22. Practice: Graph y = –2(x – 2) 2

23. Practice: Graph y = –2(x – 2) 2