Unit 8, Lesson 20

Rational and Irrational Solutions

Algebra 1

Practice

Problem 1

Student Task Statement

Decide whether each number is rational or irrational.

10
-3

Practice

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Problem 2

Student Task Statement

Here are the solutions to some quadratic equations. Select all solutions that are rational.

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Problem 3

Student Task Statement

Solve each equation. Then, determine if the solutions are rational or irrational.

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Problem 4

Student Task Statement

Here is a graph of the equation .

According to the graph, what are the solutions to the equation ?
Can you tell whether they are rational or irrational? Explain how you know.
Solve the equation using a different method and say whether the solutions are rational or irrational. Explain or show your reasoning.

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Problem 5

ForLesson 13: Completing the Square (Part 2)

Student Task Statement

Match each equation to an equivalent equation with a perfect square on one side.

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Problem 6

ForLesson 19: Deriving the Quadratic Formula

Student Task Statement

To derive the quadratic formula, we can multiply by an expression so that the coefficient of is a perfect square and the coefficient of is an even number.

Which expression, , , or , would you multiply by to get started deriving the quadratic formula?
What does the equation look like when you multiply both sides by your answer?

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Problem 7

ForLesson 12: Graphing the Standard Form (Part 1)

Student Task Statement

Here is a graph that represents .

On the same coordinate plane, sketch and label the graph that represents each equation:

<p>A curve in an x y plane, origin O.</p>

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Problem 8

ForLesson 15: Vertex Form

Student Task Statement

Which quadratic expression is in vertex form?

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Problem 9

ForLesson 10: Domain and Range (Part 1)

Student Task Statement

Function is defined by the expression .

Evaluate .
Explain why is undefined.
Give a possible domain for .

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Rational and Irrational Solutions

Practice

Problem 1

Student Task Statement

Problem 2

Student Task Statement

Problem 3

Student Task Statement

Problem 4

Student Task Statement

Problem 5

Student Task Statement

Problem 6

Student Task Statement

Problem 7

Student Task Statement

Problem 8

Student Task Statement

Problem 9

Student Task Statement

Lesson 20 Resources