# 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 ± √.