Parent Graphs of 7 Equations

This is the parent graph of a linear equation, y=x

This is the parent graph of a square root equation, y= the square root of x 

This is the parent graph of a quadratic equation, also called a parabolic equation, y=x^2

This is the parent graph of a exponential equation, y=a^x

This is the parent graph of a cubic equation, y=x^3

This is the parent graph of an absolute value equation, y= lxl 

This is the parent graph of a rational equation, y=1/x 

Squaring Numbers that End in 5

There is a simple trick to squaring numbers that end in 5, and it works no matter how large your number is!

Your first step when squaring a number that ends in 5 is to take the first digit of said number and multiply it by the number that comes after it. For example we'll use the number 45.

So, your first digit in 45 is 4

The number that comes after 4 is 5 so...

4x5=20

Now after you do that step you simply add 25 to the end of that number.

Therefore, 45^2= 2025

Changing Decimals to Fractions

There are many techniques you can use to change a decimal to a fraction. The easiest way is to just go to math and then fraction on your graphing calculator, however, it is also possible to change decimals to fractions by hand.

 First: Put the decimal over 1 in a fraction.

Second: Multiply both top and bottom by 10 for every number after the decimal point. Like, if there are two numbers after the decimal point, then use 100, if there are three then use 1000, and so on.

Lastly: Simplify your fraction.

For example, say you are given the decimal .50 

You would then put that decimal over 1

So now you have .5/1

Now multiply the top and bottom numbers of your fraction  by 100

So now you have 50/100, which you then simplify to 1/2. This is your final answer!

Rules for Exponents

When multiplying numbers with expontents be sure to only multiply numbers that have the Same Base!

 For Example, if you had x^6 and X^4 you could multiply them, because they share the same base.

However if you had x^6 and y^9 you couldn't multiply them, because their because their bases are not the same.

Here are six rules to remember when working with exponents-

1. X^m x X^n=X^m+n

2. X^m/X^n=X^m-n

3. (X^m)^n=X^mn

4. X^0=1

5. X^-n= 1/X^n

6. X^m/n =n square root of x^m



How to Identify the Dimensions of a Matrix

To identify the dimensions of a matrix first count the number of rows, then the number of columns.

For example, for the above matrix you count the number of rows (they go horizontally from left to right), and there are 3. Then you count the number of columns (they go vertically from left to right) and there are also 3. Therefore you have a 3 by 3 matrix! Any matrix with the same number of rows as columns is a perfect square matrix. 

This matrix would be a 4 by 3 matrix!

 

Systems of Equations

There are three types of systems of equations.
Consistent Independent systems when graphed intersect. The point of intersection is the solution to the system. This system has only one solution.

Consistent Dependent systems when graphed have infinitely many solutions and therefore are one line directly on top of each other.

Inconsistent Systems are systems that have NO solutions! They are parallel when graphed and never intersect.