6.1 Solving Quadratic Equations by Graphing Need Graph Paper!!!

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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

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• 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

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• Identify the quadratic term, the linear term, and
  the constant term.
• 1) 2) 3)

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

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

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

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

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

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• Assignment 6.1
• Page 339 (17-29 odd), (35- 41 odd), 49, 50, 51, 52

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6.2 Solving Quadratic Equations by Factoring

• Objective
• 1) To solve problems by factoring

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

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

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• Solve by using he zero product property.
• 7) 8)

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

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6.3 Completing the Square

• Objective
• 1) To solve quadratic equations by completing the
  square

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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)

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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)

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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)

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

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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

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

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

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Examples Value of Discriminant a Perfect Square? Nature of Roots
1 Greater than zero Yes 2 real, rational s
2 Greater than zero Yes 2 real, Irrational s
3 Less than zero na 2 imaginary s
4 Zero na 1 real
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• Find the value of the discriminant for each
  quadratic equation. Then describe the nature of
  the roots.
• 3) 4)

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

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

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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

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• 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

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

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

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• (3) Write a quadratic equation that has roots 7
  3i and 7 3i.

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

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

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• 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

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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.

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• Write the equation in the form . Then name the
  vertex, axis of symmetry, and the direction of
  the opening.
• 1) 2)

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

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• Write the equation for each parabola and then
  state the domain and range in interval notation.
• 5)

(1, 4)
(3, 4)
(2, 0)
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• Write the equation for each parabola and then
  state the domain and range in interval notation.
• 6)

(-3, 6)
(-5, 2)
(-1, 2)
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• 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)

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• 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)

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• 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)

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

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6.7 Graphing and Solving Quadratic Inequalities

• Objective
• To graph quadratic inequalities
• To solve quadratic inequalities in one variable.

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

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

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• 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

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• 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

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• 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

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

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Unit 6 ReviewExploring Quadratic Functions and
Inequalities
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• 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

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• 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