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9-12 Algebra 1 Unit 8 Lesson 19

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 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

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
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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Unit 8, Lesson 19

Deriving the Quadratic Formula

Algebra 1

Practice

Problem 1
Student Task Statement
The quadratic equation is in the form of . What are the values of , , and ?

Some steps for solving the equation by completing the square have been started here. In the third line, what might be a good reason for multiplying each side of the equation by 4?

Complete the unfinished steps, and explain what happens in these steps.

Substitute the values of , , and into the quadratic formula, , but do not evaluate any of the expressions. Explain how the expression on the right side of the equal sign is related to solving by completing the square.

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Problem 2

Student Task Statement

Consider the equation .

Does the quadratic formula work to solve this equation? Explain or show how you know.
Can you solve this equation using square roots? Explain or show how you know.

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Problem 3

Student Task Statement

Clare is deriving the quadratic formula by solving by completing the square.

She arrived at this equation.

Briefly describe what she needs to do to finish solving for , and then show the steps.

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Problem 4

ForLesson 12: Completing the Square (Part 1)

Student Task Statement

Tyler is solving the quadratic equation .

Study his work and explain the mistake he made. Then, solve the equation correctly.

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Problem 5

ForLesson 16: The Quadratic Formula

Student Task Statement

Solve the equation by using the quadratic formula. Then, check if your solutions are correct by rewriting the quadratic expression in factored form and using the zero product property.

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Problem 6

ForLesson 17: Applying the Quadratic Formula (Part 1)

Student Task Statement

A tennis ball is hit straight up in the air, and its height, in feet above the ground, is modeled by the equation , where is measured in seconds since the ball was thrown.

Find the solutions to without graphing. Show your reasoning.
What do the solutions say about the tennis ball?

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Problem 7

ForLesson 11: Graphing from the Factored Form

Student Task Statement

Consider the equation .

What are the -intercepts of the graph of this equation? Explain how you know.
What is the -coordinate of the vertex of the graph of this equation? Explain how you know.
What is the -coordinate of the vertex? Show your reasoning.
Sketch the graph of this equation.

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Lesson 19 Resources

Student Materials