Algebra II/Quadratic Functions

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A quadratic function is represented by the following equation:

2
  • 2 = Quadratic Term
  • = Linear Term
  • = Constant Term

Solving Quadratic Functions by Factoring[edit | edit source]

1. 2

  • Factor them: We get .
  • Set them out as problems to solve:
    • → x = -6
    • → x = -1
  • Your answers are and .

2. 2 .

  • Factor them: We get .
  • Set them out as problems to solve:
    • → x = -3
    • → x = 3
  • Your answers are and .

3. 2

  • Divide all of the terms by the GCF: 2: We get a new problem to deal with, which is 2.
  • Factor them: We get .
  • Set them out as problems to solve:
    • → x = -5
    • → x = -1
  • Your answers are and .

Solving Quadratic Factors by Completing the Square[edit | edit source]

1. 2 __ =

  • Take the Linear Term and divide it by : We get .
  • We take this number, , and square it: We get .
  • We add to : We get .
  • We now have: 2 .
  • We square both sides: We get .
  • We minus 4 to the other side. Here is our answer.: ± √.

2. 2 + ___

  • Take the Linear Term and divide it by : We get .
  • We take this number, , and square it: We get .
  • We have our answer: 2 + .

3. 2 =

  • Rearrange this problem so that it matches the standard format for a quadratic equation: We switch the and the around, forming our new problem: 2 = .
  • Divide the Linear Tearm, , by : This gives us .
  • Square the : This gives us .
  • Add the to : This brings our problem to ( 2 = .
  • Square both sides of the problem: This brings us to i√.
  • Find the square root of (don't forget the ) and then add to the opposite side to find your answer: Our final answer is ± .