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9 Chapter Notes

9 Chapter Notes. Algebra 1. 9-1 Notes for Algebra 1. Graphing Quadratic Functions. 9-1 pg. 550 22-56e, 81-92(x3). Quadratic Functions. (Standard Form , where ) The shape is Non-linear called a parabola Parabolas are symmetric about a central line called the axis of symmetry.

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9 Chapter Notes

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  1. 9 Chapter Notes Algebra 1

  2. 9-1 Notes for Algebra 1 Graphing Quadratic Functions

  3. 9-1 pg. 550 22-56e, 81-92(x3)

  4. Quadratic Functions (Standard Form, where ) The shape is Non-linear called a parabola Parabolas are symmetric about a central line called the axis of symmetry. The axis of symmetry intersects the parabola at only one point called the vertex.

  5. Maximum and Minimum When , the parabola opens up the vertex is called the minimum (because it is the lowest point). When , the parabola opens down the vertex is called the maximum (because it is the highest point).

  6. Graphing the parabolas To find the x-coordinate of the vertex use The is . Make a table with 2 units smaller and 2 units larger than the of the vertex, then solve for the .

  7. Example 1: Graph a parabola 1.) Use a table of values to graph . State the domain and range.

  8. Example 1: Graph a parabola 1.) Use a table of values to graph . State the domain and range. D

  9. Example 2: Identify Characteristics from Graphs Find the vertex, the equation of the axis of symmetry, and y-intercept. 1.) 2.)

  10. Example 2: Identify Characteristics from Graphs Find the vertex, the equation of the axis of symmetry, and y-intercept. 1.) 2.)

  11. Example 3: Identify Characteristics from Equations Find the vertex, the equation of the axis of symmetry and y-intercept. 1.) 2.)

  12. Example 3: Identify Characteristics from Equations Find the vertex, the equation of the axis of symmetry and y-intercept. 1.) 2.)

  13. Example 4: Maximum and Minimum Values Consider . a.) Determine whether the function has a maximum or a minimum value. b.) State the maximum or minimum value of the function. c.) State the domain and range of the function.

  14. Example 4: Maximum and Minimum Values Consider . a.) Determine whether the function has a maximum or a minimum value. b.) State the maximum or minimum value of the function. c.) State the domain and range of the function.

  15. Example 5: Graph Quadratic Functions Graph

  16. Example 5: Graph Quadratic Functions Graph

  17. Example 6: Use a Graph of a Quadratic Function ARCHERY Ben shoots an arrow. The height of the arrow can be modeled by , where represents the height in feet of the arrow seconds after it is shot into the air. 1.) Graph the height of the arrow. 2.) At what height was the arrow shot? 3.) What is the maximum height of the arrow?

  18. Example 6: Use a Graph of a Quadratic Function ARCHERY Ben shoots an arrow. The height of the arrow can be modeled by , where represents the height in feet of the arrow seconds after it is shot into the air. 1.) Graph the height of the arrow. 2.) At what height was the arrow shot? 3.) What is the maximum height of the arrow?

  19. 9-2 Algebra 1 Notes Solving Quadratic equations by graphing.

  20. 9-2 pg. 558 10-26e, 57-75(x3)

  21. Example 1: Two Roots Solve by graphing.

  22. Example 1: Two Roots Solve By graphing.

  23. Example 2: Double Root Solve By graphing.

  24. Example 2: Double Root Solve By graphing.

  25. Example 3: No Real Roots Solve by graphing.

  26. Example 3: No Real Roots Solve by graphing.

  27. Example 4: Approximate Roots with a table Solve By graphing.

  28. Example 4: Approximate Roots with a table Solve By graphing.

  29. Example 5: Approximate Roots with a Calculator MODEL ROCKETS Consuela built a model rocket for her science project. The equation models the flight of the rocket launched from ground level at a velocity of 250 feet per second, where is the height of the rocket in feet after seconds. Approximately how long was Consuela’s rocket in the air?

  30. Example 5: Approximate Roots with a Calculator MODEL ROCKETS Consuela built a model rocket for her science project. The equation models the flight of the rocket launched from ground level at a velocity of 250 feet per second, where is the height of the rocket in feet after seconds. Approximately how long was Consuela’s rocket in the air?

  31. 9-3 Notes for Algebra 1 Transformations of Quadratic Functions

  32. 9-3 pg. 569 8-28, 42-63(x3)

  33. Transformation Changes the position of size of a figure.

  34. Translation (A slide) moves a figure up, down, left or right. Vertical Translation: Horizontal Translation:

  35. Example 1: Describe and Graph Translations Describe how the graph of each function is related to the graph of 1.) 2.)

  36. Example 1: Describe and Graph Translations Describe how the graph of each function is related to the graph of 1.) 2.) translated 10 units up translated 8 units down

  37. Example 2: Horizontal Translations Describe how the graph of each function is related to the graph of 1.) 2.)

  38. Example 2: Horizontal Translations Describe how the graph of each function is related to the graph of 1.) 2.) translated 1 unit left translated 4 units right

  39. Example 3: Horizontal and Vertical Translations Describe how the graph of each function is related to the graph of 1.) 2.)

  40. Example 3: Horizontal and Vertical Translations Describe how the graph of each function is related to the graph of 1.) 2.) shifted left 1 unit and up 1 shifted right 2 units and up 6

  41. Dilation Makes a graph narrower or wider. Stretched vertically: Compressed Vertically:

  42. Example 4: Describe and Graph Dilations Describe how the graph of each function is related to the graph of 1.) 2.)

  43. Example 4: Describe and Graph Dilations Describe how the graph of each function is related to the graph of 1.) 2.) Vertically compressed Vertically Stretched and shifted up 1 unit

  44. Reflection A flip across a line. Flip over a line.

  45. Example 5: Describe and Graph Transformations Describe how the graph of each function is related to the graph of 1.) 2.)

  46. Example 5: Describe and Graph Transformations Describe how the graph of each function is related to the graph of 1.) 2.) reflected in the x-axis Compressed vertically Stretched vertically shifted down 7 units shifted up 1 unit

  47. Example 6: Identify an Equation for a Graph Which is an equation for the function shown in the graph? a.) b.) c.) d.)

  48. Example 6: Identify an Equation for a Graph Which is an equation for the function shown in the graph? a.) b.) c.) d.)

  49. 9-4 Notes for Algebra 1 Solving Quadratic equations by Completing the Square

  50. 9-4 pg. 577 10-30, 37-42, 77-81o

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