Algebra 1 Common Core Student Edition, Grade 8-9

Common Core Performance Task

Maximizing the Area of a Sign

The Ski Barn is having its annual sale. The manager asks you to order a large
rectangular sign to hang on the outside of the store. The sign must fit on a wall that
is in the shape of an isosceles triangle. The manager wants the sign to be as large
as possible so that it can be seen clearly from far away. One side of the sign will
align with the bottom of the wall, and the endpoints of the opposite side will be on
the legs of the isosceles triangle, as shown in the figure below.

12ft

Task D escr i p t i o n

Find the dimensions of the sign that will have the greatest possible area. What is
this area?

Connecting the Task to the Math Practices ^^pr aoIces

As you complete the task, you’ll apply several Standards for Mathematical
Practice.

• You'll model the height of the sign and the area of the sign with functions. (MP 4)


• You'll use a graphing calculator or other graphing utility to analyze the graph of
  the area function. (MP 5)


• You’ll consider how to use the zeros of the area function to determine the
  maximum area of the sign. (MP 2)

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