CHAPTER 9: Quadratic Equations and Functions

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CHAPTER 9Quadratic Equations and Functions

• Lesson 9.1 (Day 1)
• Solving Quadratic Equations by Finding Square
  Roots

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Square Root of a Number

• If b2 a, then b is a square root of a
• Example
• If 32 9 , then 3 is a square root of 9

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Terms

• All positive real numbers have two square roots
  (positive principal square root and a negative
  square root)
• Radical Symbol
• Radicand number or expression inside the radical
  symbol

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(No Transcript)
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Finding Square Roots of Numbers

• 64 - 64 0

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Finding Square Roots of Numbers

• 0.25 -4

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Perfect Squares

• Numbers whose square roots are integers or
  quotients of integers

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Evaluate (use a calculator if necessary)

• - 121 - 1.44 0.09 7

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Radical Expression

• An expression that involves square roots (or
  radicals)
• If symbol is in front of radical the
  expression represents two different numbers
• symbol is a grouping symbol

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Evaluate a Radical Expression

• Evaluate vb2 4ac when
• a 1 b -2 c -3

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Evaluate a Radical Expression

• Evaluate vb2 4ac when
• a 7 b 8 c 1

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Evaluating an Expression with a Calculator(round
to the nearest hundredth)
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HOMEWORK

• Page 507
• 24-50 even

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CHAPTER 9Quadratic Equations and Functions

• Lesson 9.1 (Day 2)
• Solving Quadratic Equations by Finding Square
  Roots

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Terms

• Quadratic Equation an equation that be written
  in standard form
• ax2 bx c 0 , where a ? 0
• Leading Coefficient a, when written in standard
  form
• when b 0, this equation becomes
• ax2 c 0

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Solving x2 d by finding square roots

• If d gt 0 , then x2 d has two solutions x
  d
• If d 0 , then x2 d has one solution x 0
• If d lt 0 , then x2 d has no real solutions

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Solving Quadratic Equations

• x2 4 x2 5 x2 0
  x2 -1

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Solving Quadratic Equations

• 3x2 48 0

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Solving Quadratic Equations

• x2 16 x2 11 x2 -4
  x2 100

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Solving Quadratic Equations

• x2 25 x2 81 x2 7
  x2 -12

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Solving Quadratic Equations

• 12x2 60 0

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Solving Quadratic Equations

• 120 6x2 -30

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Falling Object Model

• When an object falls the speed increases.
  Ignoring air resistance, its height h can be
  approximated by the falling object model
• h -16t2 s
• h is measured in feet
• t is the number of seconds the object has fallen
• s is the initial height from which the object was
  dropped
• -16 is the Earths gravitational pull (this
  constant would change if we were on another
  planet)

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• A student has an egg dropping contest. The goal
  is to create a container for an egg so it can be
  dropped from a height of 32 feet without breaking
  the egg. To the nearest tenth of a second, about
  how long will it take for the eggs container to
  hit the ground?
• Write an equation
• h -16t2 s

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• A student has an egg dropping contest. The goal
  is to create a container for an egg so it can be
  dropped from a height of 32 feet without breaking
  the egg. To the nearest tenth of a second, about
  how long will it take for the eggs container to
  hit the ground?
• Solve Method 1 (Make a table)
• h -16t2 32

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• A student has an egg dropping contest. The goal
  is to create a container for an egg so it can be
  dropped from a height of 32 feet without breaking
  the egg. To the nearest tenth of a second, about
  how long will it take for the eggs container to
  hit the ground?
• Solve Method 2 (Use an Equation)
• When h 0 feet
• h -16t2 32

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HOMEWORK

• Page 508
• 54-78 even, 79, 84, 86