Algebra II/Quadratic Functions

A quadratic function is represented by the following equation:

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

Solving Quadratic Functions by FactoringEdit

1.  2  

  • Factor them: We get  .
  • The linear terms must add to make 7.
  • The constant terms needs to multiply to make 6.
  • 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 SquareEdit

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  ±   .