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9-12 Integrated Math 2 Unit 5 Lesson 5

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K-5 Math 6-8 Math •9-12 Math

Course

Integrated Math 1 •Integrated Math 2 Integrated Math 3

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 Lesson 12 Lesson 13 Lesson 14 Lesson 15 Lesson 16 Lesson 17 Lesson 18 Lesson 19 Lesson 20 Lesson 21 Lesson 22 Lesson 23 Lesson 24

K-5
6-8
9-12

Integrated Math 1
Integrated Math 2
Integrated Math 3

Algebra 1
Geometry
Algebra 2
Extra Support Materials for Algebra 1

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
Lesson 12
Lesson 13
Lesson 14
Lesson 15
Lesson 16
Lesson 17
Lesson 18
Lesson 19
Lesson 20
Lesson 21
Lesson 22
Lesson 23
Lesson 24

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IM K-5 Math
IM 6-8 Math
IM 9-12 Math

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Unit 5, Lesson 5

How Many Solutions?

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Integrated Math 2

Practice

Problem 1

Student Task Statement

Rewrite each equation so that the expression on one side could be graphed and the -intercepts of the graph would show the solutions to the equation.

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Problem 2

Student Task Statement

Here are equations that define quadratic functions , and . Sketch a graph, by hand or using technology, that represents each equation.
Determine how many solutions each of , and has. Explain how you know.

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Problem 3

Student Task Statement

Mai is solving the equation . She writes that the solutions are and . Han looks at her work and disagrees. He says that only is a solution. Who do you agree with? Explain your reasoning.

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Problem 4

ForLesson 4: Solving Quadratic Equations with the Zero Product Property

Student Task Statement

If the equation is true, which is also true according to the zero product property?

Only .

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Problem 5

ForLesson 3: Solving Quadratic Equations by Reasoning

Student Task Statement

Solve the equation .
Show that your solution or solutions are correct.

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Problem 6

ForLesson 3: Solving Quadratic Equations by Reasoning

Student Task Statement

To solve the quadratic equation , Andre and Clare wrote the following:

Andre

Clare

Identify the mistake each student made.
Solve the equation, and show your reasoning.

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Problem 7

Student Task Statement

Decide if each equation has 0, 1, or 2 solutions, and explain how you know.

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Lesson 5 Resources

Student Materials

Only .

or .

or .