Polynomial Functions.

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Presentation transcript:

Polynomial Functions

Maximizing Area Area of a rectangle: A=LW Perimeter of a rectangle: P=2L + 2W If you know the perimeter, you can solve for L or W and substitute into the area formula to form a quadratic function Example: If the perimeter is 25m, write an expression for the area

Fencing in a Play area You have been hired by a local daycare to help create two areas for children to play. Both areas are to be rectangular, and a maximum of 200 ft of fencing can be used for each enclosure. One is to be attached to the side of the building, so the fencing will only be used for three sides. The other area, however, must be built with all four sides. Your job is to find the length of the sides that will produce a maximum amount of area for the children in each of the enclosures.

Draw it! If each block on your graph paper represents 20 ft, sketch the 2 play areas each with a perimeter of 200ft. What are the length, width and area of your rectangles? Draw 2 new play areas by changing your dimensions. What are the areas of the new rectangles?

Write equations! Write an equation for the perimeter of each play area. Write an equation for the area of each play yard using the perimeter.

Make a Guess! What length and width do you think will maximize the area of the full rectangular pen? What length and width do you think will maximize the area of the rectangle along the building?

Solve it! Graph the equations for area that you made by plugging in the perimeter. What type of function do you have? How can you find the maximum area of your area formula?