Intermediate Value Theorem and quadratic, applicable:

 on the interval . Is there a value of x in this interval for which the function has the value 3.

To solve this, we can see if the Intermediate Value Theorem applies. First we need the value of the function at each end of the interval so that we can decide whether the value 3 lies between them.

Since the value 3 lies between these values, we conclude that the Theorem applies and there is a value of x where the value of the function is 3.

Now let's find this value of the x coordinate, which we shall call c.

, or

The equation is satisfied by both c = 0 and c = 2. c = 0 is not in the interval, but c = 2 is, confirming that the Intermediate Value Theorem is satisfied.