Five-Minute Check (over Lesson 10–3)

Main Idea

Example 1:Graph a Cubic Funciton

Example 2:Real-World Example

• Graph cubic functions.

Graph a Cubic Function

Answer:

1. A

2. B

3. C

4. D0% 0%0%0%

Graph y = 2x3.

A. B.

C. D.

GEOMETRY Write a function for the volume V of the triangular prism below. Graph the function. Then estimate the dimensions of the prism that would give a volume of approximately 40 cubic meters.

V = Bh Volume of a prism

The function for the volume of the triangular prism is V = x3 + 4x2. Make a table of values to graph this function. You do not need to include negative values of x since the side length of the prism cannot be negative.

Looking at the graph, we see the volume of the prism is approximately 40 cubic meters when x is about 2.5 meters.

Answer: The dimensions of the prism when the volume is about 40 cubic meters are 2.5 m, 2.5 m, and (2)(2.5) + 8 or 13 m.

1. A

2. B

3. C

4. D0% 0%0%0%

A. 2 ft × 5 ft × 7 ft

B. 3 ft × 3 ft × 8 ft

C. 4 ft × 4 ft × 4 ft

D. 6 ft × 6 ft × 2 ft

A rectangular prism has a square base of side length x and a height of (x – 4) feet. Use a graph of this function to estimate the dimensions of the prism that would give a volume of about 70 cubic feet.

End of the Lesson

Five-Minute Check (over Lesson 10–3)

Image Bank

Math Tools

Area Models of Polynomials

Multiplying and Dividing Monomials

1. A

2. B

3. C

4. D0% 0%0%0%

A. 447 in2

B. 355 in2

C. 300 in2

D. 251 in2

Solve by making a model.A 15-inch by 20-inch piece of poster board has a 3.5 inch square cut out of each corner. Then the sides are folded up and taped together to make an open box. Find the surface area of the box.

(over Lesson 10-3)

1. A

2. B

3. C

4. D0% 0%0%0%

A. 251 in3

B. 364 in3

C. 560 in3

D. 1,050 in3

Solve by making a model.A 15-inch by 20-inch piece of poster board has a 3.5 inch square cut out of each corner. Then the sides are folded up and taped together to make an open box. Find the volume of the box.

(over Lesson 10-3)

1. A

2. B

3. C

4. D

0% 0%0%0%

A. 26 long tables

B. 33 long tables

C. 37 long tables

D. 44 long tables

Edward is rearranging the 132 square tables in the cafeteria to make long tables. If he uses five tables to make one long table, how many long tables can he make?

(over Lesson 10-3)

1. A

2. B

3. C

4. D

0% 0%0%0%

A. 1 table

B. 2 tables

C. 3 tables

D. 4 tables

Edward is rearranging the 132 square tables in the cafeteria to make long tables. If he uses five tables to make one long table, how many tables will be left over?

(over Lesson 10-3)

1. A

2. B

3. C

4. D

0% 0%0%0%

A. 3 cans

B. 5 cans

C. 7 cans

D. 9 cans

Kenneth is stacking 28 soup cans in a triangular pattern for a display in the school lobby. If each row has one fewer can than the row below it and finishes with one can on top, how many cans are in the bottom row?

(over Lesson 10-3)