Name____________________
Algebra I Period____________
Date_____________________
Volume and Quadratic Functions
The Lee family is building a rectangular sandbox one foot deep. Susan has decided to use lumber that is one foot wide. She collected 30 feet of lumber to enclose the sandbox.
1. Sketch a few possible sandboxes.
2. Fill in the table with some possible dimensions:
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Width |
Length |
Depth |
Volume |
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3. Predict: what do you think a scatter plot of (width, volume) will look like?
4. Enter the table value into lists in your calculator, using expression where approximate. Create a scatter plot of (width, volume) in your calculator in an approximate window and sketch:
5. Write the expression in the lists that you used for volume.
6. Enter the expression for volume into the function grapher. Sketch the graph over the scatter plot above.
7. Using your function volume: if the width of the sandbox is 3.25 feet, find the volume of sand necessary to fill the box. Solve, using your calculator:
Graphically With a Table
8. What dimensions would allow for the greatest volume of sand? Solve, using your calculator:
Graphically With a Table
9. The family decides they can afford to buy 50 ft3 of sand. What dimensions should they build the sandbox? Solve, using your calculator:
Graphically
With a Table