Curriculum  /  Math  /  9th Grade  /  Unit 7: Quadratic Functions and Solutions  /  Lesson 11

Quadratic Functions and Solutions

Lesson 11

Math

Unit 7

9th Grade

Lesson 11 of 13

Objective

Solve quadratic equations by taking square roots.

Common Core Standards

Core Standards

  • A.REI.B.4.B — Solve quadratic equations by inspection (e.g., for x² = 49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

Foundational Standards

  • 8.EE.A.2

Criteria for Success

  1. Solve equations by taking the square root and by factoring and showing that the solutions are the same. 
  2. Choose an efficient method to solve a quadratic equation based on the structure of the equation. 
  3. Solve and interpret a quadratic equation in context.
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Anchor Problems

25-30 minutes

Problem 1

A quadratic equation is shown below. 

$${x^2=(2x-9)^2}$$

a.  Solve this equation by expanding and then factoring. 

b.  Solve this equation by taking the square root of each side.

Guiding Questions

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References

Illustrative Mathematics Two Squares are Equal

Two Squares are Equal, accessed on Sept. 25, 2017, 2:47 p.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Modified by Fishtank Learning, Inc.

Problem 2

A physics teacher put a ball at the top of a ramp and let it roll down toward the floor. The class determined that the height of the ball could be represented by the equation $${h=-16t^2+4}$$, where the height, $$h$$, is measured in feet from the ground and time, $$t$$, is measured in seconds.

  1. What do you notice about the structure of the quadratic expression in this problem? 
  2. In the equation, explain what the $$4$$ represents. 
  3. Determine the time it takes for the ball to reach the floor. Interpret your solution(s) in context of the problem.

Guiding Questions

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References

EngageNY Mathematics Algebra I > Module 4 > Topic A > Lesson 6 — Example 1

Algebra I > Module 4 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Problem Set

15-20 minutes

Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task

5-10 minutes

Solve the equations.

a.  $${4a^2=16}$$

b.  $${5b^2-25=0}$$

c.  $${8-c^2=5}$$

d.  $${(x-2)^2=9}$$

e.  $$3{(x-2)^2=9}$$

f.  $${6=24(x+1)^2}$$

References

EngageNY Mathematics Algebra I > Module 4 > Topic A > Lesson 6 — Exit Ticket

Algebra I > Module 4 > Topic A > Lesson 6 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

Modified by Fishtank Learning, Inc.

Additional Practice

The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include examples where the constant value is not a perfect square root and students represent the solutions as numerical expressions involving the square root symbol

Next

Graph quadratic functions using $${x-}$$intercepts and vertex.

Lesson 12
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Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Features of Quadratic Functions

Topic B: Factoring and Solutions of Quadratic Equations

Topic C: Interpreting Solutions of Quadratic Functions in Context

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