In this section, you will use the quadratic function f(x) = a(x − h)2+ k to determine different maximum areas.

Example 3

Sandy is building a rectangular pen for her pet kittens. She can buy wire fencing in a roll of 40 feet or a roll of 80 feet. The graph shows the area of pens she can build with each type of roll.

This is the graph of two functions that shows the area of the pens using the different length of rolls.

As you look at these graphs, it is easy to assume that the transformation is a stretch. However, by looking at the vertex of each graph, the translation is not a stretch.

  1. What type of translation is seen in the graph above?

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    It is a horizontal and vertical shift.

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  2. Describe the graph of the function for a 40 ft roll of fencing as a transformation of the graph of the function for a 80 ft roll of fencing.
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    Translated 10 units left and 300 units down.

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