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

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