Differences between Linear and Quadratic Equations

Qudratic functions are expressed as \(y = x^2\) while linear expressions are expressed as \(y = x\)

Quadratic functions have \(2\) as the degree of their highest term whereas linear functions have \(1\) as their highest degree

All quadratic functions increase and decrease regradless of the slope whereas linear equations either always increase (if the slope is positive) or decrease (if the slope is negative)

The slope of a quadratic function is constantly changing. The slope of a linear function is always constant

Linear functions have each input produce a unique output. Conversely, quadratic functions (with the exception of the vertex) have pairs of unique independent variables produce the same output (ie \(x\) values of \(2\) and \(-2\) would produce the same result)

Scatter plots can also be used to identify the different relations between \(x\) and \(y\):

The relationship is considered linear when the points on a scatter plot follow a somewhat straight line pattern

The relationship is considered non-linear if the points on a scatter plot follow a pattern but not a straight line

Linear

Non-Linear

Identifying Linear and Non-Linear Equations

As stated above, a function can be determined by the degree of their highest term - also known as the Leading Term (ie a Linear Function's highest term is \(1\) while a Quadratic Function's highest term is \(2\)).
You will learn about other non-linear relations if you continue studying math!

Try and fit the following functions into their correct description: