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4 January 2010

4 January 2010. Algebra 2. Bellringer: Solve for x: 10y + 4x = 14. Notes: Graphing Quadratic Functions. Functions are equations written in the form f (x) = ______. Functions. Notes: Graphing Quadratic Functions. Functions are equations written in the form f (x) = ______

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4 January 2010

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  1. 4 January 2010 Algebra 2

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

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

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

  5. Notes: Graphing 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. Functions Quadratic Functions

  6. Notes: Graphing 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) = 2x2 + 4x – 9 Functions Quadratic Functions

  7. Notes: Graphing 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) = 2x2 + 4x – 9 Why is f(x) = x3 + x2 + 10 not quadratic? Functions Quadratic Functions

  8. Notes: Graphing 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) = 2x2 + 4x – 9 Why is f(x) = x3 + x2 + 10 not quadratic? Why is f(x) = x + 10 not quadratic? Functions Quadratic Functions

  9. Notes: Graphing Quadratic Functions Use the formula x = -b to find the vertex. 2a b = # in front of x a = # in front of x2 f(x) = 2x2 + 8x -9 x = - 8 2(2) x = -2 f(x) = 2x2 + 8x -9 f(x) = 2(-2)2 + 8(-2) -9 = -17 vertex = (-2, -17) Find the vertex of a quadratic Function Mathematics.FUN.401

  10. Notes: Graphing Quadratic Functions Using the vertex you just found, make a table of (x,y) values * put the vertex on the middle line Making a table Mathematics.GRE.605

  11. Notes: Graphing Quadratic Functions 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) Making a table Mathematics.GRE.605

  12. Notes: Graphing Quadratic Functions 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) Making a table Mathematics.GRE.605

  13. Notes: Graphing Quadratic Functions 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 Making a table Mathematics.GRE.605

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

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

  16. Guided Practice:Graph f(x) = x2 – 4x – 3

  17. 1. Find the Vertex f(x) = x2 – 4x – 3 a = ________ b = ________ x = - ( ) 2( ) x = ______

  18. 2. Evaluate x2 – 4x – 3 to find y x = _____ ( )2 – 4( ) – 3 ( )2 – 4( ) – 3 = _______  This is your y value y = _______

  19. Using the vertex you just found, make a table of (x,y) values

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

  21. Homework Find the vertex of the following equations. Then make and x/y chart using the following values for x: -3, 1, -2, 3 • 2x2-3x+5=15 • -x2+x-1=-5 • 3x2+2x+8

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