A rectangular piece of cardboard of size 16 inches by 20 inches is to be used in a factory to create boxes to transport apricots to market. The cardboard is formed into a box by cutting squares of dimensions x by x from each of the four corners and then folding up and taping the sides. The goal is to find a volume function, graph this function, and estimate the value of x that will maximize the volume of the box. a) Here is a plan view of the cardboard sheet and a three dimensional sketch of the taped box. Label the dimensions of the cutout square "x". Label the dimensions (length, width, height) of the box in terms of x. Cardboard to be cut and folded: Resulting open-top Box: 20 in 16 in b) Write a Polynomial Function, V(x), that expresses the volume of the box in terms of x only. Factor this function fully. c) Find the x and Vintercepts of this function.

A rectangular piece of cardboard of size 16 inches by 20 inches is to be used in a factory to create boxes to transport apricots to market. The cardboard is formed into a box by cutting squares of dimensions x by x from each of the four corners and then folding up and taping the sides. The goal is to find a volume function, graph this function, and estimate the value of x that will maximize the volume of the box. a) Here is a plan view of the cardboard sheet and a three dimensional sketch of the taped box. Label the dimensions of the cutout square "x". Label the dimensions (length, width, height) of the box in terms of x. Cardboard to be cut and folded: Resulting open-top Box: 20 in 16 in b) Write a Polynomial Function, V(x), that expresses the volume of the box in terms of x only. Factor this function fully. c) Find the x and Vintercepts of this function.

Algebra for College Students

10th Edition

ISBN:9781285195780

Author:Jerome E. Kaufmann, Karen L. Schwitters

Publisher:Jerome E. Kaufmann, Karen L. Schwitters

Chapter9: Polynomial And Rational Functions

Section9.4: Graphing Polynomial Functions

Problem 43PS

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