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Update Final_Exam_Study_Sheet.md
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|Type|Example|
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|Type|Example|
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|Perfect Square Trinomials| (a+b)<sup>2</sup> = a<sup>2</sup>+2ab+b<sup>2</sup> or (a-b)<sup>2</sup> = a<sup>2</sup>-2ab+b<sup></sup>|
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|Perfect Square Trinomials| $`(a+b)^2 = a^2+2ab+b^2 or (a-b)^2 = a^2-2ab+b^2`$|
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|Difference with Squares|a<sup>2</sup>-b<sup>2</sup> = (a+b)(a-b)|
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|Difference with Squares|$`a^2-b^2 = (a+b)(a-b)`$|
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|Simple Trinomials|x<sup>2</sup>+6x-7 = (x+7)(x-1)|
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|Simple Trinomials|$`x^2+6x-7 = (x+7)(x-1)`$|
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|Complex Trinomials|2x<sup>2</sup>-21x-11 = (2x+1)(x-11)|
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|Complex Trinomials|$`2x^2-21x-11 = (2x+1)(x-11)`$|
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|Common Factor|2ab+6b+4 = 2(ab+3b+2)|
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|Common Factor|$`2ab+6b+4 = 2(ab+3b+2)`$|
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|Factor By Grouping|ax+ay+bx+by = (ax+ay)+(bx+by) = a(x+y)+b(x+y) = (a+b)(x+y)|
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|Factor By Grouping|$`ax+ay+bx+by = (ax+ay)+(bx+by) = a(x+y)+b(x+y) = (a+b)(x+y)`$|
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## Shortcuts
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## Shortcuts
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- equations will have the absolute bracket be positive while the other negative.
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- equations will have the absolute bracket be positive while the other negative.
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- Absolute values are written in the form ```| x |```
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- Absolute values are written in the form ```| x |```
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- where
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- where
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- if x > 0, | x | = x
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$`
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- if x = 0, | x | = 0
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| x | =
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- if x < 0, | x | = -x
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\begin{cases}
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x, & \text{if } x > 0\\
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0, & \text{if } x = 0\\
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-x, & \text{if } x < 0
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\end{cases}
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`$
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## Quadractic Equations
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## Quadractic Equations
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- ```Quadratic Function```: A parabolic graph where the axis of symmetry is parallel to the y-axis
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- ```Quadratic Function```: A parabolic graph where the axis of symmetry is parallel to the y-axis
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- Solve quadratic equation by:
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- Solve quadratic equation by:
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1. Isolation
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1. Isolation
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- a(x+b)<sup>2</sup> + k = 0
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- $`a(x+b)^2 + k = 0`$
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2. Factor using zero-product property
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2. Factor using zero-product property
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- ```The Zero Factor Property``` refers to when a×b=0, then either a=0 or b=0.
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- ```The Zero Factor Property``` refers to when a×b=0, then either a=0 or b=0.
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- (x-a)(x-b)=0
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- $`(x-a)(x-b)=0`$
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- x = a, b
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- $`x = a, b`$
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- <img src="http://www.assignmentpoint.com/wp-content/uploads/2017/12/Quadratic-Expression-1.jpg" width="400">
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- <img src="http://www.assignmentpoint.com/wp-content/uploads/2017/12/Quadratic-Expression-1.jpg" width="400">
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