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Laabri

1.5 Graphing Absolute Value Using y = a|x-h| + k (Due 10/28/25)

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30 Nsɛmmisa
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Graphing Absolute Value Functions

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Day 2 10/28/25

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Essential Question: How can you identify the features of the graph of an absolute value function?

Learning Target: Students will be able to graph absolute value function by their features using the standard form:

y = a|x - h| + k

Show all work.

Intro to Graphing Absolute Value functions

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What is a Vertex

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8.

Describe in your own words what a vertex is.

How would you find the vertex using its graph?

How would you find the vertex using its table?

I am not looking for the right answer, I am looking for your answer.

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9.

What is the vertex of g(x). Remember to use an ordered pair (x,y) to describe it.

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10.

Use desmos to graph each function and find its vertex.

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11.

Use desmos to graph each function and find its vertex.

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12.

Use desmos to graph each function and find its vertex.

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13.

What is the equation for the translation of y = |x| that shows it moved 8 units down?

You may check your response using Desmos.

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14.

What is the equation for the translation of y = |x|that shows it moved 7 units left?

You may check your response using Desmos.

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15.

What is the equation for the translation of y = |x| 9 units right?

You may check your response using Desmos.

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16.

What is the equation for the translation of y = |x| 9 units up?

You may check your response using Desmos.

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17.

Graph the absolute value function:

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18.

Graph the absolute value function:

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19.

Graph the absolute value function:

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20.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x|

The vertex is shifted horizontally and is shifted vertically .

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21.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x|+1

The vertex is shifted horizontally and is shifted vertically .

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22.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x-3|+1

The vertex is shifted horizontally and is shifted vertically .

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23.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x+5|+2

The vertex is shifted horizontally and is shifted vertically .

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24.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x-4|-3

The vertex is shifted horizontally and is shifted vertically .

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25.

Using the form y=a|x+h|+k to graph absolute values, answer questions about the key features of this absolute value equation:

y=|x+2|

The vertex is shifted horizontally and is shifted vertically .

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26.

Match the absolute value function to its graph using its vertex.

Draggable itemarrow_right_altCorresponding Item

f(x)=|x - 2|

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f(x)=|x - 1|+1

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f(x)=|x+3|- 4

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Learning Log

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Essential Question:

What was the Essential Question of this assignment?

(Use complete sentences for full credit)

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28.

Learning Outcomes

What is one thing you learned?

(Use complete sentences for full credit)

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29.

Summarize the Topic

What was this lesson about?

(Use complete sentences for full credit)

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1.

Graph the absolute value function:

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2.

Graph the absolute value function:

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3.

Graph the absolute value function:

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4.

Graph both functions and describe how g(x) been changed from the original function: f(x)

I am not looking for the right answer, I am looking for your answer.

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5.

Describe how the absolute value function g(x) of is has been translated (moved) compared to the original function f(x)

I am not looking for the right answer, I am looking for your answer.

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6.

Graph the absolute value function:

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7.

How is the graph of y=|2x| different from the graph of y=|x|?

I am not looking for the right answer, I am looking for your answer.

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30.

1 Question I have.

1 question I have is...

(Must be a question)

OR

What was the hardest part of the assignment?