QUADRATIC FUNCTIONS Graphing And Analysis (Page 5 of 7)

For this example, the vertex is an absolute maximum. To find the coordinates of this maximum graphically, use the CALC maximum command (to find a vertex that is a minimum point use CALC minimum). You will need to answer three similar questions during this process. To set the Left Bound, enter any value of x near but a little to the left of the vertex. The Right Bound can be any value of x near but a little to the right of the vertex. For the Guess, use a value of x that is close to the vertex itself.

 2nd CALC key. 4: menu selection. 2 ENTER key. 4 ENTER key. 3 ENTER key. Calculator screen image.

We used a left bound of 2, a right bound of 4, and a guess of 3. The vertex is the point (3, 5). The coordinates of the vertex allow us to determine the range of the function, which is (-infinity, 5]. The function is increasing on the interval (-infinity, 3) and decreasing on the interval (3, infinity).
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