1. Write the function in standard form y=ax^2+bx+c. 2. Find the vertex by using the formula x=-b/2a. 3. Find the axis of symmetry by setting x=-b/2a. 4. Sketch the parabola using the vertex and axis of symmetry, opening up or down depending on whether a is positive or negative.

1. Section 10.1
GRAPH y = ax2 +c
I will graph simple quadratic functions.

3. Quadratic
Function
non linear function
that can be written
in standard form,
y = ax2 + bx + c

4. Quadratic Parabola
Function U-shaped graph that
non linear function a quadratic function
that can be written makes
in standard form,
y = ax2 + bx + c

5. Quadratic Parabola
Function U-shaped graph that
non linear function a quadratic function
that can be written makes
in standard form,
y = ax2 + bx + c

6. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes
in standard form,
y = ax2 + bx + c

7. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes
in standard form,
y = ax2 + bx + c

8. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)

9. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)

10. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)

11. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that 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

12. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)
Axis of Symmetry
the 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. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)
Axis of Symmetry
the 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. Quadratic Parabola Vertex
Function U-shaped graph that the lowest or highest
non linear function a quadratic function point on a parabola
that can be written makes The vertex of the
in standard form, parent equation
y = ax2 + bx + c y = x2 is (0,0)
Axis of Symmetry
the 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

15. Example 1

16. ★Step 1: Example 1
Make a table of
values

17. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables

18. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points

19. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points
★Step 4:
Compare the
graphs (vertex,
axis of symmetry,
vertical stretch)

20. Example 1

21. ★Step 1: Example 1
Make a table of
values

22. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables

23. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points

24. ★Step 1: Example 1
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points
★Step 4:
Compare the
graphs (vertex,
axis of symmetry,
vertical stretch)

25. Graph y = 1/2x2. Compare the
Example 2 graph with the graph of y = x2

26. Graph y = 1/2x2. Compare the
★Step 1: Example 2 graph with the graph of y = x2
Make a table of
values

27. Graph y = 1/2x2. Compare the
★Step 1: Example 2 graph with the graph of y = x2
Make a table of
values
★Step 2:
Plot the points
from the tables

28. Graph y = 1/2x2. Compare the
★Step 1: Example 2 graph with the graph of y = x2
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points

29. Graph y = 1/2x2. Compare the
★Step 1: Example 2 graph with the graph of y = x2
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points
★Step 4:
Compare the
graphs (vertex,
axis of symmetry,
vertical stretch)

30. Example 2

31. ★Step 1: Example 2
Make a table of
values

32. ★Step 1: Example 2
Make a table of
values
★Step 2:
Plot the points
from the tables

33. ★Step 1: Example 2
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points

34. ★Step 1: Example 2
Make a table of
values
★Step 2:
Plot the points
from the tables
★Step 3:
Draw a smooth
curve through
the points
★Step 4:
Compare the
graphs (vertex,
axis of symmetry,
vertical stretch)

35. 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.

36. Example 3

37. Example 3

38. Example 4

39. Example 4

40. 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.

42. Example 5

43. Example 5

44. Example 6

45. Example 6

46. Page 632
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