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2.3b Answers to questions in text.      

Activity 1

As the graphs intersect at two distinct points, we know that there must be two distinct values for  such that . Using the quadratic formula to solve we have:

Thus,

Activity 2

Now consider the case where .

First, divide through by -1 and then get one side = 0        .                                                                                                             

 So                                                         

Using the quadratic formula we have:                                 

Notice that there is only one distinct solution. This means that the graphs of  and the horizontal line  intersect at only one distinct point and that the line  is tangent to the graph of  at the point  as is shown in the following graph.

Also notice that 2 is the maximum value of  and that the maximum value occurs when . The point  is called the vertex.

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