1. 6.1 Solving Quadratic Equations by Graphing Need Graph Paper!!!
Objective:
To write functions in quadratic form
To graph quadratic functions
To solve quadratic equations by graphing

2. Vocabulary
Quadratic function-
Quadratic term-
Linear term-
Constant term-
Parabola- the graph of a quadratic function
Axis of Symmetry- a line that makes the parabola symmetric
Vertex- the minimum or maximum point of the parabola
Zeros- the x-intercepts of the parabola

3. Identify the quadratic term, the linear term, and the constant term.
1) ) 3)

4. Use the related graph of each equation to determine its solutions and find the minimum or maximum point.
1) )

5. Graph each function. Name the vertex and axis of symmetry.3)

6. Graph each function. Name the vertex and axis of symmetry.4)

7. Solve by graphing. (Find the roots)5)

8. Solve by graphing. (Find the roots)
5) (3x + 4)(2x + 7) = 0

9. Assignment 6.1
Page 339 (17-29 odd), ( odd), 49, 50, 51, 52

10. 6.2 Solving Quadratic Equations by Factoring
Objective:
1) To solve problems by factoring

11. Solve by using he zero product property.
1) 2) 3)

12. Solve by using he zero product property.
4) (3y – 5)(2y + 7) = 0 5) x(x – 1) = 0 6)

13. Solve by using he zero product property.
7) )

14. Assignment 6.2
Page 344 (11-33 odd), 41, 43, 44, 45, 46

15. Objective: 1) To solve quadratic equations by completing the square

16. Solve by completing the square.
Steps
The quadratic and linear term must be on one side of the equation and the constant must be on the other side.
The quadratic term must have a coefficient of 1.
Find c by taking half of the linear term and squaring it. 1)

17. Solve by completing the square.
Steps
The quadratic and linear term must be on one side of the equation and the constant must be on the other side.
The quadratic term must have a coefficient of 1.
Find c by taking half of the linear term and squaring it. 2)

18. Solve by completing the square.
Steps
The quadratic and linear term must be on one side of the equation and the constant must be on the other side.
The quadratic term must have a coefficient of 1.
Find c by taking half of the linear term and squaring it. 3)

21. Assignment 6.3
Page 351 (21-35 odd) 41, 43, 44, 46, 47

22. 6.4 The Quadratic Formula and the Discriminant
Objective:
To solve quadratic equations by using the quadratic formula
To use the discriminant to determine the nature of the roots of quadratic equations

23. Use quadratic formula to solve each equation.
(1.)

24. Use quadratic formula to solve each equation.
(2.)

25. Discriminant a Perfect Square?
Examples
Value of
Discriminant a Perfect Square?
Nature of Roots 1
Greater than zero
Yes
2 real, rational #’s 2
2 real,
Irrational #’s 3
Less than zero na
2 imaginary #’s 4
Zero
1 real #

26. Find the value of the discriminant for each quadratic equation
Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots.
3) 4)

27. Find the value of the discriminant for each quadratic equation
Find the value of the discriminant for each quadratic equation. Then describe the nature of the roots.
5) 6)

28. Assignment 6.4
Page 357 (17-29 odd), 34, 35, 36, 37, 38

29. 6.5 Sum and Product of Roots
Objective:
To find the sum and product of the roots of quadratic equations
To find a quadratic equation to fit a given condition

30. Quadratic equations can have up to 2 real roots (answers).
The sum and the product of these roots can be used to write a quadratic equation.
Quadratic Equation
Sum of Roots Product of Roots

31. (Denominators must be the same)
Write a quadratic equation that has roots ¾ and –12/5.
(Denominators must be the same)
Sum of Roots Product of Roots

32. (Show the easier way to solve these problems)
Write a quadratic equation that has roots 3/2 and 1/4.
(Show the easier way to solve these problems)

33. (3) Write a quadratic equation that has roots 7 – 3i and 7 + 3i.

34. (4) Write a quadratic equation that has roots 6 and -9.

35. (5) Write a quadratic equation that has roots .

36. Assignment 6.5
Page 363 (17-26), For (29-37 odd) solve each equation by using factoring, completing the square, or quadratic formula. Use each method at least once. 47, 48, 49, 51, 52

37. 6.6 Analyzing Graphs of Quadratic Functions Need Graph Paper!!!
Objective:
To graph quadratic functions of the form
2) To determine the equation of a parabola by using points on its graph.

38. Write the equation in the form
Write the equation in the form . Then name the vertex, axis of symmetry, and the direction of the opening.
1) )

39. Write the equation in the form
Write the equation in the form . Then name the vertex, axis of symmetry, and the direction of the opening.
3) )

40. Write the equation for each parabola and then state the domain and range in interval notation.5)
(1, 4)
(3, 4)
(2, 0)

41. Write the equation for each parabola and then state the domain and range in interval notation.6)
(-3, 6)
(-5, 2)
(-1, 2)

42. Write the equation for the parabola that passes through the given points.
7) (0, 0), (2, 6), (-1, 3) 8) (1, 0), (3, 38), (-2, 48)

43. Graph each function in the form
Graph each function in the form Then name the vertex, axis of symmetry, and the direction of the opening. Write the domain and range in interval notation. 9)

44. Graph each function in the form
Graph each function in the form Then name the vertex, axis of symmetry, and the direction of the opening. Write the domain and range in interval notation.
10)

45. Assignment 6.6
Page 373 (19-49 odd), 58, 62, 63, 64

46. 6.7 Graphing and Solving Quadratic Inequalities
Objective:
To graph quadratic inequalities
To solve quadratic inequalities in one variable.

47. Use the General Form to graph parabolas (Complete the Square) 1)
Vertex: ( , )
Axis of Symmetry: x=
Opening:
Left Point and Right Point (x)

48. Use the General Form to graph parabolas (Complete the Square) 2)
Vertex: ( , )
Axis of Symmetry: x=
Opening:
Left Point and Right Point (x)

49. Solve each inequality. (1) Solve of x (3) (2) Plot x’s on # line
(3) Test point in each region
(yes or no)
(4) Write inequality
(5) Write answer in interval notation

50. Solve each inequality. (1) Solve of x (4) (2) Plot x’s on # line
(3) Test point in each region
(yes or no)
(4) Write inequality
(5) Write answer in interval notation

51. Solve each inequality. (1) Solve of x
(5) (x – 1)(x + 4) (x – 3) > 0 (2) Plot x’s on # line
(3) Test point in each region
(yes or no)
(4) Write inequality
(5) Write answer in interval notation

52. Assignment 6.7
Page 382 (27-53 odd), 63, 65, 66, 67, 68, 69, 70, 71

53. Unit 6 Review Exploring Quadratic Functions and Inequalities

54. Unit 6 Test is worth 100 points
Covers sections 6.1 – 6.7
Study notes and hw
Unit 6 Test Review
Page 400 (11-53 odd)
Page 357 (19, 23, 27)
Page 382 (39, 47, 51)
Page 352 (41)- worth 18 points on test

55. Sum and Product of Roots
Items on the Test
Quadratic function
Quadratic term
Linear term
Constant term
Parabola
Axis of Symmetry
Vertex
Zeros
Completing the Square
Quadratic Formula
Discriminant
Sum and Product of Roots
Domain
Range
Interval Notation
Intercepts
Quadratic Inequalities