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9-12 Algebra 2 Unit 3 Lesson 1

Gradeband

K-5 Math 6-8 Math •9-12 Math

Course

Algebra 1 Geometry •Algebra 2 Extra Support Materials for Algebra 1

Unit

Unit 1 Unit 2 •Unit 3 Unit 4 Unit 5 Unit 6 Unit 7 Unit 8

Modeling Prompts

Lesson

•Lesson 1 Lesson 2 Lesson 3 Lesson 4 Lesson 5 Lesson 6 Lesson 7 Lesson 8 Lesson 9 Lesson 10 Lesson 11

K-5
6-8
9-12

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

Integrated Math 1
Integrated Math 2
Integrated Math 3

Unit 1
Unit 2
Unit 3
Unit 4
Unit 5
Unit 6
Unit 7
Unit 8

Modeling Prompts

Lesson 1
Lesson 2
Lesson 3
Lesson 4
Lesson 5
Lesson 6
Lesson 7
Lesson 8
Lesson 9
Lesson 10
Lesson 11

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Unit 3, Lesson 1

Minimizing Surface Area

Algebra 2

Practice

Problem 1
Student Task Statement
There are many cylinders with a volume of cubic inches. The height , in inches, of one of these cylinders is a function of its radius , in inches, where .

What is the height of one of these cylinders if its radius is 2 inches?

What is the height of one of these cylinders if its radius is 3 inches?

What is the height of one of these cylinders if its radius is 6 inches?

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Problem 2

Student Task Statement

The surface area , in square units, of a cylinder with a volume of 18 cubic units is a function of its radius , in units, where . What is the surface area of a cylinder with a volume of 18 cubic units and a radius of 3 units?

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Problem 3

Student Task Statement

Han finds an expression for that gives the surface area, in square inches, of any cylindrical can with a specific fixed volume, in terms of its radius , in inches. This is the graph Han gets if he allows to take on any value between -1 and 5.

What would be a more appropriate domain for Han to use instead?
What is the approximate minimum surface area for the can?

<p>graph of y = S of r. vertical asymptote at x = 0. function decreasing to the left of asymptote. function decreases until y = 16 and then increases to the right of asymptote.</p>

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Problem 4

ForLesson 8: End Behavior (Part 1)

Student Task Statement

The graph of a polynomial function is shown. Is the degree of the polynomial even or odd? Explain your reasoning.

<p>polynomial function graphed. x intercepts = -3, -1, 1, 3. y intercept = 9. f of x increases as x increases in both the positive and negative direction.</p>

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Problem 5

ForLesson 12: Polynomial Division (Part 1)

Student Task Statement

The polynomial function has known factors of and .

Rewrite as the product of linear factors.
Draw a rough sketch of the graph of the function.

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Problem 6

ForLesson 15: The Remainder Theorem

Student Task Statement

Which polynomial has as a factor?

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Lesson 1 Resources

Student Materials