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NYS COMMON CORE MATHEMATICS CURRICULUM M4 Lesson 6 ALGEBRA I Lesson 6: Solving Basic One-Variable Quadratic Equations S.1 This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0- 09.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unpor Lesson 6: Solving Basic One-Variable Quadratic Equations Classwork Example 1 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 ( t)=−16 t 2 +4 , where the height, h ( t), is measured in feet from the ground and time, t, is measured in seconds. a. What do you notice about the structure of the quadratic expression in this problem? b. In the equation, explain what the 4 represents. c. Explain how you would use the equation to determine the time it takes the ball to reach the floor.

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Page 1: Algebra › ... › 3 › 870334… · Web vieweat Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike

ALGEBRA I

Lesson 6: Solving Basic One-Variable Quadratic Equations S.1This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

Lesson 6: Solving Basic One-Variable Quadratic Equations

Classwork

Example 1

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( t)=−16 t 2+4, where the height, h( t), is measured in feet from the ground and time, t , is measured in seconds.

a. What do you notice about the structure of the quadratic expression in this problem?

b. In the equation, explain what the 4 represents.

c. Explain how you would use the equation to determine the time it takes the ball to reach the floor.

d. Now consider the two solutions for t . Which one is reasonable? Does the final answer make sense based on this context? Explain.

Lesson 6 M4NYS COMMON CORE MATHEMATICS CURRICULUM

Page 2: Algebra › ... › 3 › 870334… · Web vieweat Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike

ALGEBRA I

Lesson 6: Solving Basic One-Variable Quadratic Equations S.2This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

2. The length of a rectangle is 5∈. more than twice a number. The width is 4∈. less than the same number. The perimeter of the rectangle is 44∈¿. Sketch a diagram of this situation, and find the unknown number.

3. The length of a rectangle is 5∈. more than twice a number. The width is 4∈. less than the same number. If the

area of the rectangle is 15¿2, find the unknown number.

ExercisesSolve each equation. Some of them may have radicals in their solutions.

1. 3 x2−9=0 2. (x−3)2=1 3.

4 (x−3)2=1

Lesson 6 M4NYS COMMON CORE MATHEMATICS CURRICULUM

Page 3: Algebra › ... › 3 › 870334… · Web vieweat Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015 This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike

ALGEBRA I

Lesson 6: Solving Basic One-Variable Quadratic Equations S.3This work is derived from Eureka Math ™ and licensed by Great Minds. ©2015 Great Minds. eureka-math.org This file derived from ALG I-M4-TE-1.3.0-09.2015

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License.

ExercisesSolve the following problems. Be sure to indicate if a solution is to be rejected based on the contextual situation.

4. The length of a rectangle is 4 cm more than 3 times its width. If the area of the rectangle is 15cm2, find the width.

5. The ratio of length to width in a rectangle is 2 ∶ 3. Find the length of the rectangle when the area is 150¿2.

Lesson 6 M4NYS COMMON CORE MATHEMATICS CURRICULUM