Converting from a linear system of equations to an augmented matrix involved bringing down the coefficients of equations down in a particular way. It is important that

1. Each column in your augmented matrix only has coefficients from one variables.
2. One row of your augmented matrix has coefficients from only one of the equations.

0:00 Introduction
0:08 System of linear equations for first augmented matrix
1:54 Disordered system of linear equations to convert to augmented matrix

#augmentedmatrix
#matrices
#joecmath

The Pythagorean Theorem relates the lengths of the sides of a right triangle with the following formula:

a^2+b^2=c^2

Where a and b are legs of the triangle and c is the hypotenuse.

#PythagoreanTheorem
#RightTriangle
#JoeCMath
#Trig

0:00 Intro
0:10 Define triangle sides and Pythagorean Theorem
0:50 Example 1
1:55 Example 2
3:23 Example 3
4:00 Example 4
4:48 3 types of problems and their solutions formula

A quick video that explains how to identify and combine like terms within an algebraic expression. This is part of a series in which my goal is to deliver short information dense videos on small topics within mathematics.

Terms are considered like if they:
1. Have the same variables.
2. The power/degree of each variable agrees.

#CombineLikeTerms
#JoeCMath

0:00 Introduction
0:12 Like terms checklist and classification
1:32 Simplifying an expression with like terms
2:00 S+U+B+S+C+R+I+B+E=2(S+B)+U+C+R+I+E

Having trouble finding the area under a given normal curve or distribution? Unsure of how to proceed?

This video quickly introduces two methods for solving homework problems of involving finding the percent of the normal curve above or below a point as well as between two given points.

0:00 Set up to normal distribution problem
0:15 z-score approach to solving problem
0:41 Using standard deviation normal distribution template
1:31 Using quartile normal distribution template

#normaldistribution
#normalcurve
#mathoverview
#joecmath
#statistics

The process of completing the square for a quadratic expression, equation, or function can seem confusing at first.

What do you do when a=1?

What do you when a is not 1?

Well, with the method discussed it doesn't matter what value of a you are working with.


#CompletingTheSquare
#CompleteTheSquare
#StandardtoVertex
#Algebra
#JoeCMath

0:00 Introduction
0:18 Potentially confusing moment, nothing to see here.
0:30 Example 1
2:44 General form beside Example 1
4:20 Example 2
5:40 Interact with channel implies Joe makes more content.

Six examples that require the simplification/combination of exponents using exponent properties are provided with a step-by-step process for simplification.

The four properties that are the main focus in this video are the product, power, quotient, and negative exponent properties. Individual videos for each one of these properties can be found on my channel.


#Exponents
#Simplifying
#MathExamples
#JoeCMath
#ExponentRules
#ExponentProperties

0:00 Introduction
0:15 Easy Example 1
1:51 Easy Example 2
4:02 Easy Example 3
5:44 Medium Example 1
8:17 Medium Example 2
10:55 Hard Example ONLY
15:01 Subscribe if this was helpful!

The first quartile of the normal distribution is found at the mean -0.67 times the standard deviation. The third quartile is found at the mean +0.67 times the standard deviation.

The first quartile, the mean, and the third quartile break down the normal distribution into approximately four equal parts each containing about 25% of the distribution.

The problems involving this breakdown of the normal distribution either use the word quartile or talk about 25, 50, or 75 % of the distribution within the question.

Some images used were generated using Geogebra.

0:00 Introduction
0:11 First Quartile
0:18 Third Quartile
0:24 How the quartiles break up normal curve
0:39 Type of problems using normal distribution quartiles

#quartiles
#normaldistribution
#statistics
#JoeCMath

The end behavior of a polynomial tells us the direction a function goes as x approaches positive or negative infinity. Using just the coefficient and highest power of a polynomial we can determine the end behavior.

Some images made using Geogebra.

0:00 Introduction
0:20 End behavior of 6x^4+5x^3-2x^2+x-20
1:48 The four types of polynomial end behaviors
3:14 End behavior of -0.5x^5+5x^2-x+1
4:03 End behavior of 2x^3-x^6+2x^7+2
4:47 Starting with graph and working backwards

#polynomialendbehavior
#polynomials
#graphingpolynomials
#JoeCMath
#precalculus

Factoring the difference of two squares can be done quickly as long as you can rewrite your expression equation or function in the form a^2-b^2. The factored form will then be (a+b)(a-b).

a^2-b^2=(a+b)(a-b)


#DifferenceOfSquares
#DifferenceofTwoSquare
#Factoring
#Algebra
#JoeCMath

0:00 Introduction
1:00 Example 1
1:39 Example 2
2:16 Example 3
2:35 Example 4
3:18 Yeah... I didn't have a good idea for an outro.

A quick video that relates the Zero Product Property to finding solutions to a factored polynomial.


#ZeroProductProperty
#Solutions
#JoeCMath

0:00 Introduction
0:22 The zero product property
0:40 Example that uses the zero product property
1:39 Zero product property for more than two factors
2:00 Honestly, the best thing I have ever made!

Details the process of completing the square for a quadratic expression. Two examples are given to motivate the process.


#CompletingTheSquare
#a=1
#StandardtoVertex
#Algebra
#JoeCMath

0:00 Introduction
0:32 General process of completing the square.
1:22 Example 1
3:29 Example 2
4:30 Consider subscribing

Finding the y-intercept of a function is easy if you are given the graph, but how do you find it if you are given only a function in a single variable?

Some images made using Geogebra.

#y-intercept
#Findy-int
#JoeCMath
#y-int
#verticalintercept
#yint

0:00 Introduction
0:08 Finding the y-intercept when given the graph
1:40 Steps to find the y-intercept of a function
2:45 What? No unnecessary math outro?

When you have variables of a common base multiplied together you can simplify it by adding the powers of the variables together and writing it as a single term.

The rule
x^m*x^n=x^(m+n)


#Simplify #MultiplyingVariables #ExponentProperties
#JoeCMath

0:00 Introduction
0:14 Example of Property
0:49 Example 1
1:07 Example 2
1:49 Word of caution
2:08 You should hit that Subscribe button

A quick and easy to follow guide to using FOIL to multiply two binomials together. I repeat, TWO BINOMIALS TOGETHER! FOIL is of no use for anything other than that!


#FOIL
#First-Outer
#Inner-Last

0:00 Introuction
0:18 When to use FOIL with example
1:55 JoeCMath in a Park (Part 1)

Multiplying matrices can be tricky. Not every pair of matrices can be multiplied together. Also, for a given pair of matrices, the order in which one multiplies matters as well. This video goes over the basics you need to know in order to successfully identify matrices that can be multiplied together as well as how to do matrix multiplication.

0:00 Introduction
0:10 When can I multiply matrices?
2:11 Example 1 Starts
5:47 Prelude to Example 2
7:41 Example 2 Starts
10:16 Review Questions

#matrixmultiplication
#matrixmath
#joecmath

Graphing a quadratic function in vertex form can be done easily when you understand the following:

What does the "a" value tell us about the quadratic function?
How to find the y-intercept?
How to find the vertex?
How to find the x-intercepts?

Some images made using Geogebra.

#VertexForm
#GraphingQuadratics
#GraphingParabola
#VertexFormtoGraph
#JoeCMath

0:00 Introduction
0:20 General steps to graph vertex form
1:12 Example 1
4:16 Example 2
6:16 Did you subscribe?

Sometimes, you are asked to make sure all of the exponents in your answer are positive. To convert any exponent from negative to positive you either move the variable from the numerator to the denominator or you move the variable from the denominator to the numerator. You may have heard this rule called the elevator rule, because you can imagine the variable hopping into an elevator and moving up or down one floor.

The rule is:

x^(-n)=1/x^n
or
1/x^(-n)=x^n

0:00 Introduction
0:21 Where the rule comes from
1:52 Example 1
2:08 Example 2
2:25 Example 3
3:35 Warning for multiple term problems
4:12 Subscribe to bring Joe some joy

#NegativeExponents
#NegativePowers
#ExponentRules
#JoeCMath
#Exponents
#Powers

Finding all of the missing lengths and angles of a right triangle can be confusing. With SOHCAHTOA, the Pythagorean Theorem, and Interior Angle Sum methods being hard to identify when to use each to find what you are looking for.

The examples in this video were chosen to help explain when to use the three methods and talks about the expected result of each method.

#SolveRightTriangle
#geometry
#JoeCMath
#trigonometry
#trig
#missingtriangleside
#missingtrianglelength

0:00 Introduce and Label Example 1
1:13 Example 1 Starts
5:05 Methods Review
6:10 Introduce and Label Example 2
7:15 Example 2 Starts
10:22 Path of Least Pain by Problem Setup

Knowing which factoring procedure to use when factoring a quadratic can be hard, but when a=1, there is a simple process detailed in this video that can be used to factor the quadratic expression, equation, or function you are working with.

To see more examples for this process please check out: "https://youtu.be/mrOcBddblPo"

#Factoring
#Algebra
#JoeCMath

0:00 Introduction
0:30 Process for factoring when a=1
2:16 Example of factoring when a=1
6:45 Takeaways
7:10 Subscribe for more JoeCMath videos!

After finding the sign chart for your polynomial, first, and second derivatives you may lose sight of what they all represent.

The sign chart of your polynomial will tell you when your function value, f(x), is above (positive on sign chart) or below (negative on sign chart) the x-axis.

The sign chart of your first derivative tells you when your function is increasing (positive on first derivative sign chart) or decreasing (negative on first derivative sign chart).

The sign chart of your second derivative tells you when your function is concave up (positive on second derivative sign chart) or concave down (negative on second derivative sign chart).


0:00 Introduction
0:25 Interpreting the Polynomial Function Sign Chart
1:54 Interpreting the First Derivative Sign Chart
3:28 Interpreting the Second Derivative Sign Chart
4:30 Four possible combinations of First and Second Derivative Sign Chart patterns
4:42 Making sense of all three sign charts together
7:12 Using the template found using the sign charts in unison with graph of polynomial


#polynomial
#polynomialfunctions
#signchart
#joecmath