Do Now: Simplify Each Expression x(-2 – x) (-2x – x^2)

12.1 QUADRATIC FUNCTIONS SWBAT explore properties of parabolas using example of parabolas from the real world.

Example: A dog trainer is fencing in an enclosure, represented by the shaded region in the diagram. The trainer will also have two square-shaped storage units on either side of the enclosure to store equipment and other materials. She can make the enclosure and storage units as wide as she wants, but she can’t exceed 100 feet in total length.

Apply the Distribute Property

Sketch the Quadratic Function Calculate dependent values A(s) given the independent s s A(s) = -2s^2 + 100s

Sketch the graph, label the axes and intervals Sketch the graph, label the axes and intervals. How can you tell the graph is a quadratic function?

Parabola

According to the graph, is there a maximum area that the enclosure can contain? Yes, The highest point on the parabola is (25, 1250). The y-value represents area so the max area is 1250 sq. ft. Determine the dimensions (length x width) of the enclosure that will provide the maximum area. Show your work and explain your reasoning. Since the highest pt. on the parabola is (25, 1250) and the x-value represents the width of 25 and max area is 1250 sq. ft. A = lw 1250 = 25l The dimension is 25x50 ft. 50 = l