1. 3 January 2010 Algebra 2

2. Bellringer: Solve for x: 10 + 4x = 14

3. Agenda: Progress Report Information Classroom Standards and Expectations Graphing Quadratic Functions Exit Ticket

4. Progress Report Information

5. Classroom Standards and Expectations

6. Notes: Graphing Quadratic Functions FunctionsFunctions are equations written in the form f(x) = ______

7. Notes: Graphing Quadratic Functions FunctionsFunctions are equations written in the form f(x) = ______ Example: f(x) = 5 or f(x) = 3x + 9

8. Notes: Graphing Quadratic Functions Functions Quadratic Functions Functions are equations written in the form f(x) = ______ Example: f(x) = 5 or f(x) = 3x + 9 Quadratic functions are functions that have a degree of 2.

9. Notes: Graphing Quadratic Functions Functions Quadratic Functions Functions are equations written in the form f(x) = ______ Example: f(x) = 5 or f(x) = 3x + 9 Quadratic functions are functions that have a degree of 2. Example: f(x) = 2x 2 + 4x – 9

10. Notes: Graphing Quadratic Functions Functions Quadratic Functions Functions are equations written in the form f(x) = ______ Example: f(x) = 5 or f(x) = 3x + 9 Quadratic functions are functions that have a degree of 2. Example: f(x) = 2x 2 + 4x – 9 Why is f(x) = x 3 + x 2 + 10 not quadratic?

11. Notes: Graphing Quadratic Functions Functions Quadratic Functions Functions are equations written in the form f(x) = ______ Example: f(x) = 5 or f(x) = 3x + 9 Quadratic functions are functions that have a degree of 2. Example: f(x) = 2x 2 + 4x – 9 Why is f(x) = x 3 + x 2 + 10 not quadratic? Why is f(x) = x + 10 not quadratic?

12. Notes: Graphing Quadratic Functions Find the vertex of a quadratic Function Mathematics.FUN.401 Use the formula x = -b to find the vertex. 2a b = # in front of x a = # in front of x 2 f(x) = 2x 2 + 8x -9 x = - 8 2(2) x = -2 f(x) = 2x 2 + 8x -9 f(x) = 2(-2) 2 + 8(-2) -9 = -17 vertex = (-2, -17)

13. Notes: Graphing Quadratic Functions Making a table Mathematics.GRE.605 Using the vertex you just found, make a table of (x,y) values * put the vertex on the middle line x2x 2 + 8x - 9y(x,y) -22(-2) 2 + 8(-2) -9-17(-2, -17)

14. Notes: Graphing Quadratic Functions Making a table Mathematics.GRE.605 Using the vertex you just found, make a table of (x,y) values * pick any two numbers greater than the x value of your vertex (-2) x2x 2 + 8x - 9y(x,y) 0 -22(-2) 2 + 8(-2) -9-17(-2, -17)

15. Notes: Graphing Quadratic Functions Making a table Mathematics.GRE.605 Using the vertex you just found, make a table of (x,y) values * pick any two numbers less than the x value of your vertex (-2) x2x 2 + 8x - 9y(x,y) 0 -22(-2) 2 + 8(-2) -9-17(-2, -17) -3 -4

16. Notes: Graphing Quadratic Functions Making a table Mathematics.GRE.605 Using the vertex you just found, make a table of (x,y) values * complete the rest of the table by substituting your x values into your function x2x 2 + 8x - 9y(x,y) 02(0) 2 + 8(0) -9-9(0,-9) 2(-1) 2 + 8(-1) -9-15(-1,-15) -22(-2) 2 + 8(-2) -9-17(-2, -17) -32(-3) 2 + 8(-3) -9-15(-3,-15) -42(-4) 2 + 8(-4) -9-9(-4,-9)

17. Notes: Graphing Quadratic Functions Graphing a Q.F. Mathematics.GRE.605 Using the (x,y) pairs you just found, plot the points on a graph. (0,-9) (-1,-15) (-2, -17) (-3,-15) (-4,-9)

18. Notes: Graphing Quadratic Functions Graphing a Q.F. Mathematics.GRE.605 Connect the five points you have plotted. PHEW, Finally done!!!!!

19. Guided Practice: Graph f(x) = x 2 – 4x – 3

20. 1. Find the Vertex f(x) = x 2 – 4x – 3 a = ________b = ________ x = - ( ) 2( )x = ______

21. 2. Evaluate x 2 – 4x – 3 to find y x = _____( )2 – 4( ) – 3 ( )2 – 4( ) – 3 = _______  This is your y value y = _______

22. Using the vertex you just found, make a table of (x,y) values xx 2 – 4x – 3y(x,y) 2(2) 2 – 4(2) - 3-7(2, -7)

23. 4. List the 5 points you are going to graph: _______, _______, __(2,-7)_, _______, _______