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Find c by taking half of the linear term and squaring it. Assignment 6.3 ... Discriminant a Perfect Square? Examples ... (Complete the Square) 1) Vertex: ... – PowerPoint PPT presentation

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Title: 6'1 Solving Quadratic Equations by Graphing Need Graph Paper


1
6.1 Solving Quadratic Equations by GraphingNeed
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) 2) 3)

4
  • Use the related graph of each equation to
    determine its solutions and find the minimum or
    maximum point.
  • 1) 2)

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), (35- 41 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) 8)

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

15
6.3 Completing the Square
  • 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)

19
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20
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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
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26
  • 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. 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
  • Write a quadratic equation that has roots ¾ and
    12/5.
  • (Denominators must be the same)

Sum of Roots Product of Roots
32
  • 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 FunctionsNeed
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 . Then name the
    vertex, axis of symmetry, and the direction of
    the opening.
  • 1) 2)

39
  • Write the equation in the form . Then name the
    vertex, axis of symmetry, and the direction of
    the opening.
  • 3) 4)

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 . 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 .
    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 xs 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 xs 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) gt 0 (2) Plot xs 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 ReviewExploring 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
  • 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
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