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

A video detailing how to use the quadratic formula to find solutions to quadratic equations and x-intercepts of quadratic functions.

#QuadraticFormula
#Algebra
#JoeCMath

0:00 Introduction
0:14 Quadratic formula used for what?
0:45 Steps for using quadratic formula
1:24 Example of using quadratic formula
3:41 Review of video
4:04 Your subscription forces me to smile for 1 second!

z-scores are helpful because they allow us to make inferences about any normal distribution by converting points or values of interest to a value, z, in the standard normal distribution (mean is zero and standard deviation is one).

We can use a z-table to look up z-scores and determine the percent of the distribution above or below the z-score and then relate it back to the distribution we start with.

Also, z-scores are a measure of how many standard distributions a number is away from the mean.

Images used in this video were created using GeoGebra.

0:00 The value of z-scores
0:47 Area under distribution example
2:39 Standard deviation measurement example
3:35 Summary of two topics in video

#zscore
#normaldistribution
#statistics
#joecmath

A horizontal shift of a function occurs when a constant is added or subtracted within the input location (where you enter your values into your variable on the right hand side of a function).

The rules for how much you shift a function horizontally and the direction you shift a function sometimes feel out of thin air.

This video attempts to provide some context for the rules that students normally commit to memory for horizontal shifts.

0:00 Introduction
0:06 Usual rules for horizontal shifts
0:22 Introduction to shifting approach
0:59 Horizontal shift of x^2 example
3:01 Horizontal shift of absolute value function
4:14 When x is multiplied by a constant in the input
4:34 Revisiting the rules from the beginning of the video
5:13 Identifying a horizontal shift in a function with more than one shift and scaling factors

#horizontalshift
#functiontranslation
#JoeCMath

Two examples of using the quadratic formula. One example solves for x within a quadratic equation. The other finds the x-intercepts of a quadratic function.

#QuadraticFormula
#Solutions
#JoeCMath

0:00 Introduction
0:12 When do we use the quadratic formula
0:37 Scenario definition
1:11 Using quadratic formula with quadratic equation
2:55 Finding x-intercept of quadratic function
4:54 I dare you to subscribe!

Summations (sigma notation) is used to represent a large sum of terms that follow a pattern. In calculus you will learn about series, which are sums with an infinite number of terms. But before you get to that, you need to understand the basic notation.

A common example provided in the video is the sum of 1 through 100. Also, a short introduction to the sum of 1 through some positive natural number n is discussed.

0:00 Introduction
0:09 Basic components of summation notation
0:37 Basic Example: Summing i from 1 to 3
1:27 How summation notation compacts large sums
1:56 Example: Summing i^2 from 1 to 5
2:43 Summing natural numbers from 1 to n
3:50 Using closed form solution to sum from 1 to 100
4:40 Warnings for things I didn't talk about
4:45 Any letter can be your index of summation
5:10 You can have a sum of variables
5:33 You can sum over sets
6:03 Hammering in the message

#summation
#sigmanotation
#sums
#joecmath
#calculus

Short, edited, easy to follow math tutorials for high school and college subjects. Consider watching some videos and subscribing to support the channel!

#maths
#mathhelpers
#joecmath
#mathchannel
#mathyoutuber
#mathhelp
#highschoolmath
#collegemath

As long as you have factored your polynomial completely, making a sign chart of the base function, first derivative, or second derivative of a polynomial follows a similar process every time.

A walkthrough of the process if shown first in the video followed by a list of steps that were followed to help one reproduce a sign chart on their own.

0:00 Introduction
0:21 Polynomial used in video
1:01 Finding the x-intercepts of polynomial
1:57 Breaking up number line using zeros (x-intercepts)
2:20 Picking test points from each interval on number line
2:49 Plugging test points into the binomials
3:50 Understanding the row of signs in a sign chart
4:39 Getting the final sign for each section
5:49 Interpreting the sign chart
6:44 Reviewing the steps for creating sign chart

#polynomials
#signchart
#polynomial
#JoeCMath

Graphing a horizontal line of the form y=a where "a" is as easy as finding the value "a" on the y-axis and drawing a horizontal line at that location. It can be easy to confuse y=a with x=a, but remember that y=a is the equation for a horizontal line.

Some images made using Geogebra.

#HorizontalLines
#Graphing
#JoeCMath

0:00 Introduction
0:09 Graphing y=1
1:41 Graphing y=-2, y=-1, y=0, and y=2
2:00 Every subscription matters

The graphs of x=a or y=a can be confusing. The graphs of x=a equations will be a vertical line while the graphs of y=a equations will be a horizontal line.

Some images made using Geogebra.

#VerticalLines
#Graphing
#JoeCMath

0:00 Introduction
0:12 Graphing x=2
1:53 Graphing x=-3, x=-2, x=-1, x=0, x=1, and x=3
2:11 A waste of my time -JoeCMath

Getting from JoeCMath 1.0 to JoeCMath 2.0 by improving math video quality!


I have been happy with my production style so far, but feel that I can and should still improve the quality of my videos. There is a Math YouTube channel 3Blue1Brown, created by Grant Sanderson, that hosts easily the best math videos on YouTube. Naturally, I have been researching how Grant accomplishes this and it turns out it is through a collection of Python and other various files that he calls Manim.

For my 100 subscriber video, I spent time learning some of the basics of Manim and put together my first video using it. I am excited about the future Manim videos that I create, as they can only improve from here!

#100subs
#QualityFocused
#FirstManimVideo
#JoeCMath

0:00 Introduction
0:20 Improving Quality of Videos
1:22 What is Manim?
2:17 Thanks for subscribing!!!

First off, I'd like to thank everyone that has subscribed and supported my channel in it's first year on YouTube. I had set some rather crazy goals that I fell short of but allow me to better plan out 2021 and future years.

I was surprised that there were a decent number of people that were sharing my content in the first year! This channel is something I have had knocking around in my head ever since 2015 (after tutoring math non-stop for four years and teaching for two years), and so I am mostly proud of just finally getting started.

I am quite excited about the future of this channel! Let's make 2021 a great year!

#FirstYearOnYouTube
#JoeCMath
#YouTubeGoals

0:00 Introduction
0:10 2020 YouTube goal review
0:52 2021 YouTube Goals
1:34 My focus in 2021
2:20 Going over share data for 2020
3:12 Conversation about 2020 videos that had good views

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