1. Pick up and do the Bellwork Quiz 9-2. (1-6) Only

2. To be able to SKETCH the graph of a quadratic equation.
Today’s Objective
To be able to SKETCH the graph of a quadratic equation.
Take Notes when you see this icon….

3. y = ax2 +bx + c Quadratic Functions
Quadratic functions are equations of the form …..
y = ax2 +bx + c
Where a, b, and c are real numbers and a is not zero.

4. y = ax2 +bx + c Quadratic Functions And Finally the whole #
Then comes the x term
And Finally the whole #
x2 term is always first

5. Find the values for a, b, and c in the following:
1.) y = 2x2 -5x + 12
a = 2, b= -5, c = 12
2.) y = 6 - x2 + 3x
2.) y = - x2 + 3x + 6
a = -1, b= 3, c = 6

6. Quadratic Functions
The graph of a quadratic function is U shaped and is called a parabola.
The end of the parabola is called the Vertex.

7. Quadratic Functions
The line the U is wrapped around is called the Axis of Symmetry.

8. Consider the graph of y = x2
Parabola Y X
Axis of
Symmetry
Vertex
(0,0)

9. Quadratic Equations of the form: y = ax2 +bx + c
1.) If a is positive, the U is up.
2.) If a is negative, the U is down.
3.) The Vertex has an x-coordinate of -b/2a.

10. Now Lets Graph y = x2 - 2x - 3 1.) Make a T-Table.
2.) Pick 5 x values that are small, some negative, and don’t forget 0.

11. Now we will plug them into the equation
y = x2 - 2x - 3
Now we will plug them into the equation x y -3 -1 1 3

12. y = x2 - 2x - 3
y = (-3)2 - 2(-3) - 3
y =
y = 12 12

13. y = x2 - 2x - 3
y = (-1)2 - 2(-1) - 3
y =
y = 0 12

14. y = x2 - 2x - 3
y = (0)2 - 2(0) - 3
y = - 3 12 -3

15. y = x2 - 2x - 3
y = (1)2 - 2(1) - 3
y =
y = -4 12 -3 -4

16. y = x2 - 2x - 3
y = (3)2 - 2(3) - 3
y =
y = 0 12 -3 -4

17. y = x2 - 2x - 3 Y X
Vertex
(1,-4)

18. y = x2 - 2x - 3 Use -b/2a to find the x coordinate of the vertex.
-(-2)/2(1) = 2/2 = 1
The axis of symmetry is the line x = -b/2a, So….
X = 1 is the axis of symmetry.

19. y = x2 - 2x - 3 Y X
Vertex
(1,-4)
Axis of
Symmetry

20. You Try it, graph y = x2 - 2x - 5 1.) Make a T-Table.
2.) Pick 5 x values that are small, some negative, and don’t forget 0.

21. Now we will plug them into the equation
y = x2 - 2x - 5
Now we will plug them into the equation x y -3 -1 1 3

22. y = x2 - 2x - 5
y = (-3)2 - 2(-3) - 5
y =
y = 10 10

23. y = x2 - 2x - 5
y = (-1)2 - 2(-1) - 5
y =
y = -2 10 -2

24. y = x2 - 2x - 5
y = (0)2 - 2(0) - 5
y = - 5 10 -2 -5

25. y = x2 - 2x - 5
y = (1)2 - 2(1) - 5
y =
y = -6 10 -2 -5 -6

26. y = x2 - 2x - 5 y = (3)2 - 2(3) - 5 y = 9 - 6 - 5 y = -2 10 -2 -5 -6

27. y = x2 - 2x - 5 Y X
Vertex
(1,-6)

28. y = x2 - 2x - 5 Now find the x coordinate using -b/2a
- (-2)/2(1) = 2/2 = 1

29. Bellwork, Graph y = x2 + 4x + 3 1.) Make a T-Table.
2.) Pick 5 x values that are small, some negative, and don’t forget 0.

30. Now we will plug them into the equation
y = x2 + 4x + 3
Now we will plug them into the equation x y -3 -1 1 3

31. y = x2 + 4x + 3 x y -3 -1 3 8 1 24 3

32. y = x2 + 4x + 3 Y X

33. Today’s Objective
To be able to SKETCH the graph of a quadratic equation and find the Vertex.

34. y = ax2 +bx + c Quadratic Functions
Quadratic functions are equations of the form …..
y = ax2 +bx + c
Where a, b, and c are real numbers and a is not zero.

35. y = ax2 +bx + c Quadratic Functions And Finally the whole #
Then comes the x term
And Finally the whole #
x2 term is always first

36. y = the equation with the x value plugged in
Finding the Vertex
x = -b/2a
y = the equation with the x value plugged in

37. Find the x coordinate using -b/2a, then find the y coordinate.
1.) y = x2 + 4x + 3
2.) y = x2 + 3x - 7

38. y = 4 - 8 + 3 y = -1 Vertex = (-2,-1) x = - (4)/2(1) = -2
1.) y = x2 + 4x + 3
x = - (4)/2(1) = -2
y = x2 + 4x + 3
y = (-2)2 + 4(-2) + 3
y =
y = -1 Vertex = (-2,-1)

39. 2.) y = x2 + 3x - 7 y = 9/4 - 9/2 - 7 y = -9 1/4 (-3/2,-9 1/4)

40. Find the x coordinate using -b/2a, then find the y coordinate.
1.) y = x2 + 2x - 8
2.) y = x2 - 3x - 4

41. y = 1 - 2 - 8 y = -9 Vertex = (-1,-9) 1.) y = x2 + 2x - 8

42. 2.) y = x2 - 3x - 4 y = 9/4 - 9/2 - 4 y = -6 1/4 (3/2,-6 1/4)

43. Do the quadratic graphing worksheet
Classwork
Do the quadratic graphing worksheet

44. Try these graphs
1.) y = x2 - 3x - 4
2.) y = x2 + 3x - 7

45. 1.) y = x2 - 3x - 4 Y X

46. 1.) y = x2 - 3x - 4 y = 9/4 - 9/2 - 4 y = 4 (3/2,-6 1/4)
- (-3)/2(1) = 3/2
1.) y = x2 - 3x - 4
1.) y = (3/2)2 - 3(3/2) - 4
y = 9/4 - 9/2 - 4
y = (3/2,-6 1/4)

47. 2.) y = x2 + 3x - 7 y = 9/4 - 9/2 - 7 y = 4 (-3/2,-9 1/4)
- (3)/2(1) = -3/2
1.) y = x2 + 3x - 7
1.) y = (-3/2)2 + 3(-3/2) - 7
y = 9/4 - 9/2 - 7
y = (-3/2,-9 1/4)

48. Rewrite each equation in standard form …..
1.) 9 = 2x2 -5x + 12
0 = 2x2 -5x + 3
2.) 3 = 6 - x2 + 3x
0 = - x2 + 3x + 3