From 50e7bd45e8e7d85341703a6e9a86908ad52ecc81 Mon Sep 17 00:00:00 2001
From: James Su <amagicalsoup@gmail.com>
Date: Thu, 18 Apr 2019 16:25:34 +0000
Subject: [PATCH] Update Final_Exam_Study_Sheet.md

---
 Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md | 29 +++++++++++--------
 1 file changed, 17 insertions(+), 12 deletions(-)

diff --git a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md
index 0e936a1..14a0c1b 100644
--- a/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md	
+++ b/Grade 9/Math/MPM1DZ/Final_Exam_Study_Sheet.md	
@@ -194,12 +194,12 @@
 
  |Type|Example|
  |:--:|:-----:|
- |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>|
- |Difference with Squares|a<sup>2</sup>-b<sup>2</sup> = (a+b)(a-b)|
- |Simple Trinomials|x<sup>2</sup>+6x-7 = (x+7)(x-1)|
- |Complex Trinomials|2x<sup>2</sup>-21x-11 = (2x+1)(x-11)|
- |Common Factor|2ab+6b+4 = 2(ab+3b+2)|
- |Factor By Grouping|ax+ay+bx+by = (ax+ay)+(bx+by) = a(x+y)+b(x+y) = (a+b)(x+y)|
+ |Perfect Square Trinomials| $`(a+b)^2 = a^2+2ab+b^2 or (a-b)^2 = a^2-2ab+b^2`$|
+ |Difference with Squares|$`a^2-b^2 = (a+b)(a-b)`$|
+ |Simple Trinomials|$`x^2+6x-7 = (x+7)(x-1)`$|
+ |Complex Trinomials|$`2x^2-21x-11 = (2x+1)(x-11)`$|
+ |Common Factor|$`2ab+6b+4 = 2(ab+3b+2)`$|
+ |Factor By Grouping|$`ax+ay+bx+by = (ax+ay)+(bx+by) = a(x+y)+b(x+y) = (a+b)(x+y)`$|
 
 ## Shortcuts
 
@@ -235,9 +235,14 @@
 - equations will have the absolute bracket be positive while the other negative.   
 - Absolute values are written in the form ```| x |```
 - where    
-  - if x > 0, | x | = x   
-  - if x = 0, | x | = 0    
-  - if x < 0, | x | = -x
+$`
+| x | =
+\begin{cases}
+x, & \text{if  } x > 0\\
+0, & \text{if  } x = 0\\
+-x, & \text{if  } x < 0
+\end{cases}
+`$
 
 ## Quadractic Equations
 - ```Quadratic Function```: A parabolic graph where the axis of symmetry is parallel to the y-axis    
@@ -245,11 +250,11 @@
 - Solve quadratic equation by:    
 
   1. Isolation    
-     - a(x+b)<sup>2</sup> + k = 0
+     - $`a(x+b)^2 + k = 0`$
   2. Factor using zero-product property    
      - ```The Zero Factor Property``` refers to when a&times;b=0, then either a=0 or b=0.     
-     - (x-a)(x-b)=0    
-     - x = a, b      
+     - $`(x-a)(x-b)=0`$    
+     - $`x = a, b`$      
 
 - <img src="http://www.assignmentpoint.com/wp-content/uploads/2017/12/Quadratic-Expression-1.jpg" width="400">