Unit 2, Lesson 1

Let’s Make a Box

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Integrated Math 3

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Problem 1

A rectangular schoolyard is to be fenced in using the wall of the school for one side and 150 meters of fencing for the other three sides. The area $A(x)$ in square meters of the schoolyard is a function of the length $x$, in meters, of each of the sides perpendicular to the school wall.

Write an expression for $A(x)$.
What is the area of the schoolyard when $x=40$?
What is a reasonable domain for $A$ in this context?

Problem 2

Noah finds an expression for $V(x) $ that gives the volume of an open-top box in cubic inches in terms of the length $x$ in inches of the cutout squares used to make it. This is the graph Noah gets if he allows $x$ to be any value between -1 and 5.

<p>Noah's graph. crosses origin, increasing from 0 to 1, maximum at 15, decreasing from 1 to 3. increasing to the right of 3. x intercepts at 0, 2 point 5 and 3 point 5. </p>

What would be a more appropriate domain for Noah to use instead?
What is the approximate maximum volume for his box?

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