9.5 Solving by Factoring

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9.5 Solving by Factoring

• Algebra 14.0, 23.0

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Predicting with Evidence

• What are the zeros for
• y x2 x 6?

• Now factor x2 x 6 0 and solve. What do you
  notice about the graph and our factored
  solutions?
• What does this mean?

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Main Idea

• For the rest of the chapter, we are going to
  learn different methods to solve a quadratic
  equation, besides graphing.
• Instead of graphing a parabola to find the zeros,
  we are going to learn ways to find the zeros,
  which are solutions.
• Today, we are going to use our chapter 8 skills
  to factor a quadratic equation. By breaking it
  down, we can find the zeros!

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Zero Product Property

• Zero Product Property if the product equals
  zero, then one of the values must equal zero.
• This property helps to find our ZEROS.
• Meaning Our quadratic equation must equal 0 in
  order to find the zeros by solving.

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Ex 1-Using the Zero ProductProperty

• These quadratic equations are already factored,
  so finish by setting each factor equal to 0 and
  solve.

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Practice 1
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Example 2 Solving by Factoring

• Solving by factoring
• Write the quadratic equation in standard form y
  ax2 bx c OR ax2 bx c 0
• Factor the quadratic equation (chapter 8)
• Use the Zero Product Property to set each factor
  to 0 and solve.
• The answers are your zeros on the graph!

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Ex 2- Solving Quadratic EquationsBy Factoring
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Ex 2- Solving Quadratic EquationsBy Factoring
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Practice 2
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Ex 3 Sports Application

• Same steps
• Write in standard form
• Factor
• Solve each factor to find the zeros!

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Practice 3
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Review

• What are you trying to find when you graph or
  solve quadratic equations?
• What is the zero product property? How does it
  help you solve?
• How do you know if your solutions are correct?