Math 10.1

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  • Math 10.1

    1. 1. Section 10.1GRAPH y = ax2 +cI will graph simple quadratic functions.
    2. 2. Quadratic Functionnon linear functionthat can be written in standard form, y = ax2 + bx + c
    3. 3. Quadratic Parabola Function U-shaped graph thatnon linear function a quadratic functionthat can be written makes in standard form, y = ax2 + bx + c
    4. 4. Quadratic Parabola Function U-shaped graph thatnon linear function a quadratic functionthat can be written makes in standard form, y = ax2 + bx + c
    5. 5. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes in standard form, y = ax2 + bx + c
    6. 6. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes in standard form, y = ax2 + bx + c
    7. 7. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
    8. 8. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
    9. 9. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0)
    10. 10. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Parent Quadratic Function the most basic quadratic equation, y = x2
    11. 11. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
    12. 12. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
    13. 13. Quadratic Parabola Vertex Function U-shaped graph that the lowest or highestnon linear function a quadratic function point on a parabolathat can be written makes The vertex of the in standard form, parent equation y = ax2 + bx + c y = x2 is (0,0) Axis of Symmetrythe line that passes through the vertex and divides the parabola in two symmetrical parts. The a of s of y = x2 is x=0 Parent Quadratic Function the most basic quadratic equation, y = x2
    14. 14. Example 1
    15. 15. ★Step 1: Example 1Make a table ofvalues
    16. 16. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables
    17. 17. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
    18. 18. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
    19. 19. Example 1
    20. 20. ★Step 1: Example 1Make a table ofvalues
    21. 21. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables
    22. 22. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
    23. 23. ★Step 1: Example 1Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
    24. 24. Graph y = 1/2x2. Compare theExample 2 graph with the graph of y = x2
    25. 25. Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues
    26. 26. Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables
    27. 27. Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
    28. 28. Graph y = 1/2x2. Compare the★Step 1: Example 2 graph with the graph of y = x2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
    29. 29. Example 2
    30. 30. ★Step 1: Example 2Make a table ofvalues
    31. 31. ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables
    32. 32. ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points
    33. 33. ★Step 1: Example 2Make a table ofvalues★Step 2:Plot the pointsfrom the tables★Step 3:Draw a smoothcurve throughthe points★Step 4:Compare thegraphs (vertex,axis of symmetry,vertical stretch)
    34. 34. Comparing to y=x 2When |a|>1, then there is a vertical stretch, by a factor of a.When |a|<1, then there is a vertical shrink, by a factor of a. When a is negative, whether a>1 or a<1, then there is a reflection in the x-axis.
    35. 35. Example 3
    36. 36. Example 3
    37. 37. Example 4
    38. 38. Example 4
    39. 39. Comparing to y=x 2 When |a|>1, then there is a vertical stretch, by a factor of a. When |a|<1, then there is a vertical shrink, by a factor of a.When a is negative, whether a>1 or a<1, then there is a reflection in the x-axis.When c is positive, then there is a vertical translation up c units.When c is negative, then there is a vertical translation down c units.
    40. 40. Example 5
    41. 41. Example 5
    42. 42. Example 6
    43. 43. Example 6
    44. 44. Page 632# 3-5,6,10,14,18,22,23,24,27,33,37

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