:( Algrebra 1 I CAN #9- Performance Task: Backyard with Quadratics .
Task 1: A home improvment show is designing a backyard for a family. They want to install a regtangular pool in the center of the backyard. It will have two equal square sections of grass on each side of the pool the same width as the pool.
The entire length of the backyard is 40 feet. Let w represent the width of each square section of grass. What width, w, would allow the family to get the maximum area out of their pool design.
a. Sketch the backyard design and label your sketch.
b. Write an expression to represent the length of the pool.
c. Write the function A(w) to represent the area of the pool as a function of the width, w, only. Hint: Use your expression in part b and remember, Area= length x width.
d. Graph your function with technology (desmos) to determine the absolute maximum of this function. Sketch your graph below and lable the maximum point. (Be sure to also lable and scale your axes!)
e. Use your maximum point to answer the original question: What width, w, would allow the family to get the maximum area out of their pool design?
f. What is the maximum area for the pool?