Åk 6–9

5.1 Nonlinear Functions
This is a function which differs from the earlier ones.

y = x2 - 4

As you see here the one x-variable has the exponent 2.  It is called a second degree function.

How does the graph of a second degree function look like?

We begin by choosing a few values of x and making a value table:

We show this with a graph in the coordinate system by plotting in the points and connecting them.

In the coordinate system you can clearly see that the graph doesn’t make a straight line, and it is as such not a linear function. What is special with second degree functions is that:

  • they have a maximum value (highest value) or a minimum value (lowest value) for y. In the example above, the function has a minimum value.  What determines if it has a max- or minimum value is if the m-value in the second degree function is positive or negative? A positive m-value gives a minimum value on the y-axis and a negative m-value gives a max value.

    If you want to freshen up your memory about what m-value is, you can read page 4.2

  • for each value of y there can be two values of x. This applies for all second degree functions. The exception is the max and minimum values.