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Academia Internacional de Baltimore

巴尔的摩国际学校 ةيلودلا روميتلاب ةيميداكأ

Балтиморская Интернациональная Академия

Académie Internationale de Baltimore

Baltimore International Academy

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Algebra I Packet May 18 - May 22, 2020

BIA Weekly Instructional Plan Middle School Algebra 1

Week of: May 18 – May 22

MYP Subject Monday Tuesday Wednesday Thursday Friday Algebra 1

Module 4

Topic B Using

different forms

for quadratic

functions

L16: Graphing Quadratic Equations

from the Vertex Form, 𝑦 = 𝑎(𝑥 − ℎ)2 +

𝑘 .

Graphing quadratics: vertex

form

L17 : Graphing Quadratic

Functions from the Standard Form,

𝑓(𝑥) = 𝑎x2 + 𝑏x + 𝑐.

Graphing quadratics: standard

form

Review

Online

Resources/Pla

tform

Course materials including lessons, practices, classworks, and answer

keys are posted on Google classroom.

Khan Academy

Kutasoftware

o Eureka Knowledge on the Go – 15-45min https://gm.greatminds.org/en-us/knowledge-for-grade-9

o facilitated by Great Minds

o available online, by phone, or channel 77 & Charm City TV

Добро пожаловать Bienvenidos

NYS COMMON CORE MATHEMATICS CURRICULUM M4 Lesson 16

ALGEBRA I

𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘 Lesson 16: Graphing Quadratic Equations from the Vertex Form,

S.90

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 Unported License.

Problem Set

1. Find the vertex of the graphs of the following quadratic equations.

a. 𝑦 = 2(𝑥 − 5)2 + 3.5

b. 𝑦 = −(𝑥 + 1)2 − 8

2. Write a quadratic equation to represent a function with the following vertex. Use a leading coefficient

other than 1.

a. (100, 200)

b. (−34

, −6)

3. Use vocabulary from this lesson (i.e., stretch, shrink, opens up, and opens down) to compare and contrast the

graphs of the quadratic equations 𝑦 = 𝑥2 + 1 and 𝑦 = −2𝑥2 + 1.

Lesson Summary

When graphing a quadratic equation in vertex form, 𝑦 = 𝑎(𝑥 − ℎ)2 + 𝑘, (ℎ, 𝑘) are the coordinates of the vertex.

NYS COMMON CORE MATHEMATICS CURRICULUM M4 Lesson 17

ALGEBRA I

𝑓(𝑥) = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Lesson 17: Graphing Quadratic Functions from the Standard Form,

S.98

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 Unported License.

Problem Set

1. Graph 𝑓(𝑥) = 𝑥2 − 2𝑥 − 15, and identify its key features.

Lesson Summary

The standard form of a quadratic function is 𝑓(𝑥) = 𝑎𝑥2 + 𝑏𝑥 + 𝑐, where 𝑎 ≠ 0. A general strategy to graphing a

quadratic function from the standard form:

Look for hints in the function’s equation for general shape, direction, and 𝑦-intercept.

Solve 𝑓(𝑥) = 0 to find the 𝑥-intercepts by factoring, completing the square, or using the quadratic

formula.

Find the vertex by completing the square or using symmetry. Find the axis of symmetry and the

𝑥-coordinate of the vertex using –𝑏

2𝑎 and the 𝑦-coordinate of the vertex by finding 𝑓 (

–𝑏2𝑎

).

Plot the points that you know (at least three are required for a unique quadratic function), sketch the

graph of the curve that connects them, and identify the key features of the graph.

NYS COMMON CORE MATHEMATICS CURRICULUM M4 Lesson 17

ALGEBRA I

𝑓(𝑥) = 𝑎𝑥2 + 𝑏𝑥 + 𝑐 Lesson 17: Graphing Quadratic Functions from the Standard Form,

S.99

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 Unported License.

2. Graph 𝑓(𝑥) = −𝑥2 + 2𝑥 + 15, and identify its key features.

3. Did you recognize the numbers in the first two problems? The equation in the second problem is the product of −1

and the first equation. What effect did multiplying the equation by −1 have on the graph?

4. Giselle wants to run a tutoring program over the summer. She comes up with the following profit function:

𝑃(𝑥) = −2𝑥2 + 100𝑥 − 25

where 𝑥 represents the price of the program. Between what two prices should she charge to make a profit? How

much should she charge her students if she wants to make the most profit?

5. Doug wants to start a physical therapy practice. His financial advisor comes up with the following profit function for

his business:

𝑃(𝑥) = −12

𝑥2 + 150𝑥 − 10000

where 𝑥 represents the amount, in dollars, that he charges his clients. How much will it cost for him to start the

business? What should he charge his clients to make the most profit?