Upcoming SlideShare
×

# Math 10.1

452 views
393 views

Published on

0 Likes
Statistics
Notes
• Full Name
Comment goes here.

Are you sure you want to Yes No
• Be the first to comment

• Be the first to like this

Views
Total views
452
On SlideShare
0
From Embeds
0
Number of Embeds
28
Actions
Shares
0
8
0
Likes
0
Embeds 0
No embeds

No notes for slide
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• \n
• ### 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