here's algebra one explained in just ten minutes first of all what is algebra it is the study of symbols and the rules what is a math symbol it is a variable and that is a placeholder so variables can be called x y z a b and we don't know what's inside but what we do know is that expressions are multiple symbols and variables placed together but what if you add an equal sign both sides must stay balanced voila now we have something that's called an equation because of the equal sign and to solve equations you would do the goal is to isolate the variable and solve for the value let's go order of operations with pride if you see a minus sign you add and if it's multiply you divide and sometimes it is possible to have x on both sides and what you would do in this case is to treat excess something that also has to be balanced just like the rest of the stuff in the equation but what happens if you have two variables it becomes a function what is a function you put a value in and you get a value out the value that you put into a function is known as x and it is called an independent variable because you have control over what x equals you could pass in any value of x and the value that comes out is called y and y is known as the dependent variable because its value depends on what x's value is of course there could be many different letter combinations but x and y are the most common on the coordinate plane the x-axis is where the independent variable is and the y-axis is where the dependent variable is the x-intercept is where the function intersects the x-axis and the y-intercept is where the the graph intersects the y-axis but you have to keep in mind that if there's an easy way to prove that a function is a function and it's called the vertical line test you graph the function you draw a vertical line if there's any two points that intersect with that vertical line you know that you do not have a function you can plug in random values of x to get their y values but what is a way that we can determine all the possible x and y values for a function it's called [Music] if you have a function that's continuous meaning that there's no holes or gaps here's how to find the domain and range [Music] ring functions that may have holes or gaps in them instead are called piecewise functions and how you would find the domain and range of those is you could plot it on a graph or you could look at all the different pieces and find out where certain values and points are left out we're now going to take a quick intermission and talk about our sponsor maplesoft if you feel absolutely unprepared for algebra 1 eoc keep listening a huge part of the algebra 1 eoc is related to graphing linear functions systems of equations inequalities and everything that we just covered practice and patterns are important to help you get a good score get easy graphing practice using the maple calculator open the app and click on the pencil icon plot any equation and a graph will appear below it plotting the equation next visit the check mark icon to see how to plot the equation how to solve for x and you get a table and some even allow you to see a 3d model of your graph which is pretty fun have fun graphing by downloading both the calculator and maple learn in our description below let's now get into the main functions that you should know to succeed in algebra 1. the first one is called a linear function it's a straight line i'm gonna be fine i'm pretty sure y'all are familiar with the phrase miles per hour uh hour is the independent variable and miles is the dependent variable and the relationship between these two can be represented as how steep a linear function is how do we determine the steepness of a graph it's called slope and what you do next is x another name for slope is linear equations always have a constant slope and there are three different ways that you could write a linear equation exhibit a slope intercept form why is i'm x plus b y is mx plus b and the slope of the line well b is the y intercept y is mx plus b y is mx plus b these four parts are fine to graph a line exhibit b point slope form [Music] lastly here's standard form these are all the parts of standard form [Music] keep in mind that you cannot have fractions and a cannot equal zero so that wraps up three forms of linear equations now what do we want to do if we want to find out where two linear functions intersect we now have system of equations if you have a calculator just graph both equations and see where they intersect simple easy but it's good to know the other ways to do it as well method one is substitution to solve an equation using substitution you would write one variable in terms of the other so if you have y equals x plus five wherever you see y you just replace it with x plus 5 solve for x and then plug that x back in and then solve for y [Music] to solve using elimination you just eliminate one of the variables so you line up both equations that both coefficients and and letters match and then you have to try to figure out some way to cancel out one of them solve for one of the letters and plug it back in to solve for the other one before we wrap up linear functions let's talk about linear inequalities i mentioned that linear equations have to be equal to each other on both sides but that's not necessarily true with an inequality you have greater than less than greater than or equal to or less than or equal to and you basically follow what the sign says and here is how to graph and shade linear inequalities on a graph [Music] if the symbol does not have an equal to sign draw a dash line [Music] shape of all the light [Music] here is the second main function that you have to know we have linear functions but what happens if we take x and we multiply it by itself it becomes x squared and this is the basis of a quadratic function and unlike linear functions these aren't lines all of these are u-shapes and they have an infinite domain just like the linear functions but the range is limited because a u shape has either a maximum point or a minimum point depending on whether it's facing upward or downward there are three different forms of quadratic functions vertex standard and factored form each form has their own advantages and disadvantages the vertex form helps you find the vertex which is h comma k for standard form 0 c is the y intercept and negative b over 2a is the x value of the axis of symmetry which is where the graph splits in half factored form helps you find your zeros your roots and it's also called your x-intercepts so how do you solve for the zeros the first step is you could obviously graph it if you have a calculator and see where it intersects the x-axis and obviously we cannot forget x is equal to negative b plus or minus the square root of b squared minus four ac all over two and another popular method is factoring and due to the sake of time i can't explain all the steps but the maple calculator does a pretty good job of explaining it once you put an equation in and you can check our video about factoring which i'll link right here the last thing i'm going to cover for quadratic functions is how can we tell how many solutions a quadratic function has it's simple you just have to find what the discriminant is and the discriminant is basically equal to b squared minus 4ac here's how to make sense of it if it's greater than [Music] the last type of function i'm going to cover is called an exponential function and what's different about this function is that you have some random number at any number as the base and then x is your exponent so you can plug in any value of x into that into that exponent the domain of an exponential function is all real numbers but notice that the range is not exactly like that because in this example the y is slowly approaching zero but it never reaches zero this particular example is called a horizontal asymptote an asymptote occurs when a graph tries to reach a certain value and gets really close but never reaches it there are horizontal vertical and slant asymptotes also make sure to remember all the rules of exponents thank you so much for watching this video i hope it helped if you like learning math through songs definitely subscribe to our channel and check out our patreon and also don't forget to download the maple calculator the link is in our description goodbye