Quadratic equations function in the same manner as linear equations in that you have a particular input resulting in a particular output. You plot points on the graph in the same manner as you do linear equations. The difference is that the graph of a quadratic forms a curved line, called a parabola, instead [...]

The line graphs generated by linear equations are not limited to the portion of the graph shown, but instead continue on infinitely in either direction. Essentially, you are working with a segment of the line graph and a few of the points it contains. We can further analyze the measurements of these line segments [...]

A graph, or coordinate plane, can be used to represent the results of equations by plotting their inputs and outputs. Basically, a value is inputted into an equation (with one variable), a series of mathematical actions occur, and a single output is created. A graph is made up of two perpendicular number lines, called the [...]

So far, you have mostly been solving for a single variable in an equation or placing one variable in terms of the others. However, you will likely face questions asking you to solve for more than one variable, and these questions will likely be about linear equations. A linear equation simply refers to an [...]

You know that 2 is a larger number than 1, and you know that ‐2 is a smaller number than ‐1, so how do you show both of these statements to be true? While an equation is a demonstration of two quantities equal to one another, inequalities demonstrate two quantities not equal to one [...]

Direct and inverse variation refers to two values that are proportional to one another depending on a particular constant, or k: Direct variation multiplies the constant to one of the values. Inverse variation divides the constant by one of the values. To determine which variation to use, look closely at the words used in [...]

Absolute value, represented as a vertical line on either side of the value, refers to a number or variable’s distance from zero on the number line. There are always two numbers that share the same distance from zero: a positive number and its negative counterpart. The absolute value for a variable will usually result [...]

The idea of the equation shouldn’t be new to you. We’ve already covered several concepts where an action results in a specific value. If you recall, there is always an equal sign between the action and the result, which is a statement that one expression is equal to the other. Since algebraic expressions can [...]

Since we can multiply algebraic expressions we can factor them out. While the process of factoring is different than using a factor tree, the concept is the same. You are looking for what parts make up the whole algebraic expression. Think of factoring as the reverse of multiplying algebraic expressions. Factoring out algebraic expressions [...]

Algebraic expressions are not solely made up of coefficients and a single variable. Algebraic expressions can be made up of multiple terms, which are either added or subtracted from each other. These terms can include several distinct variables, their coefficients, and known quantities called constants. Depending on their number of terms, algebraic expressions can [...]