This week in pre calc 11 we started chapter 4, and the first thing we learned was properties of quadratic functions. Now it’s important that before we start listing off the properties of each of these quadratic functions, that we know 100% that this is a quadratic equation. How can we tell if a function is linear, quadratic, or neither. In this blogpost I’m going to show you how you can tell the difference between a quadratic function and a linear function by looking at the table of values for any type of function.

Linear – look at the first differences, if they are equal to each other than it is a linear function.

Quadratic – Look at the second differences, if they are equal to each other than it is a quadratic function.

Neither – Than it just simply doesn’t follow any of the rules from above and is not a linear or quadratic function.

Ok so lets begin, suppose we have this table given to us:

The first step is to find the first difference, how you do this is to find how much space is between each of the #s.

As you can see, the first differences are equal to each other therefor this is a linear function.

Let’s look at another example:

Follow the same steps as you did for the function above:

As you can see, the first differences aren’t equal to each other so now we have to find the second differences:

The second differences are equal! Therefor this is a quadratic function.

Lets look at one last example:

First – find the first differences:

The first differences aren’t equal so we move on to step 2 – finding the second differences:

For this example both the first and second differences are not equal therefor this is neither a quadratic or linear function.