U2 L4 Identifying Key

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Algebra I

August 26, 2024

Unit 2: Introduction to Functions
Lesson 4: Identifying Key Attributes

9

LO:SWBAT identify the x-intercepts, y-intercepts, and zeros in
mathematical and real-world problems using the graph of
linear, quadratic, and exponential functions on the coordinate
plane.

DOL: Given a set of problems, students will correctly identify
the x-intercepts, y-intercepts, and zeros in mathematical and
real-world problems using the graph of linear, quadratic, and
exponential functions on the coordinate plane in at least 4 of 5
questions.

ALGI.3C Graph linear functions on the coordinate plane and identify key features, including x-intercept, y-intercept, zeros, and slope, in mathematical
and real-world problems.
ALGI.7A Graph quadratic functions on the coordinate plane and use the graph to identify key attributes, if possible, including x-intercept, y-intercept,
zeros, maximum value, minimum values, vertex, and the equation of the axis of symmetry.
ALGI.9D Graph exponential functions that model growth and decay and identify key features, including y-intercept and asymptote, in mathematical
and real-world problems.

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Lesson Vocabulary

x-intercept or zeros

y-intercept

Essential Question

11

How can you
identify the
x-intercepts,
zeros, and
y-intercepts of a
function?

I can identify the x-intercepts, zeros,
and y-intercepts of a function by…

13

The maintenance crew at a park is draining the swimming pool.
The graph shows the number of gallons in the pool, y, as it
drains for x hours.

Gallons Remaining

Hours

Pool by Clker-Free-Vector-Images from Pixabay

How many gallons of water did the pool begin

with?

The pool began with 500 gallons of water. We
see from the graph that is where the function
begins.

This point is called the y-intercept because it is
where the line crosses the y-axis.

Multiple Choice

Maria graphed a function with a y-intercept of 4. Which of the graphs could represent Maria’s function?

•  

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Maria graphed a function with a y-intercept of 4.
Which of the graphs could represent Maria’s function?

B

C

A

Drag and Drop

Mr. Sims gave his students the graph of an exponential function. What are the x and y-intercepts of the function?



y - intercept : ​ (​ ​

Placeholder

, ​ ​

Placeholder

)

x - intercept :​ (

Placeholder

, ​

Placeholder

)

Drag these tiles and drop them in the correct blank above

19

Mr. Edmonds graphed the quadratic equation y = −x2 + 3x + 5 for
his students. What are the zeros of the function?

When identifying the zeros of this

function, I see that I can only

estimate the values.

If we want to know the exact
values, our calculator will be

helpful.

Let’s go to:

www.desmos.com/testing/texas/graphing

Multiple Select

 Carla graphed a quadratic function. Which values represent the zeros of the function?

• x = 1

• x = −4

• x = −1

• x = 3

• x = 0

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Open Desmos and type this function in a new line.

You may start the
function with y =

or with f (x) =.

Multiple Choice

Robert graphed the function $$y=5x−7$$ on the coordinate plane. What is the zero of the function?

• 7

• 1.4

• 5

• 2.2

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For any graph, Desmos will automatically mark important points
like intercepts.

Click on the

intercepts and
Desmos will tell

you the

coordinates.

What are the zeros of the function?

(−1.193, 0)
(4.193, 0)

Math Response

The number of stores opened by a coffee company is modeled on the graph. How many stores did the coffee company begin with?

Type answer here

Correct Answer: 400

Deg^°

Rad

Multiple Choice

Heather graphed a function with one zero and a y-intercept of 2. Which of the following graphs can represent Heather’s graph?

Dropdown

The graph shows the height in feet of an object above the ground t seconds after it was launched from the ground. How long did it take the object hit the ground?​

​

Select answer

seconds

Math Response

Jason graphed a linear function. What is the y-intercept of the function?

Type answer here

Correct Answer: 5

Deg^°

Rad

Math Response

Sandra has the following function on her math homework.

$$y=\frac{1}{2}x^2-3x-1$$

What is the negative zero of the function? round to the nearest thousandths place.

Type answer here

Correct Answer: -.317

Deg^°

Rad

A. $25

B. $50

C. $200

D. $75

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Brad babysits each week to save for new headphones. He
deposits the money in his savings account. Brad’s saving
account balance is shown on the graph. What is the beginning
balance of Brad’s savings account?

Weeks

Account Balance

Multiple Choice

Brad babysits each week to save for new headphones. He deposits the money in his savings account. Brad’s saving account balance is shown on the graph. What is the beginning balance of Brad’s savings account?

• $25

• $50

• $200

• $75

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Ms. Henderson gave her students a list of functions.
Which functions have the same zeros? Select TWO correct
answers.

A.

y = x2 − 4x + 4

B.

y = x+ 2

C.

y = −4x + 3

D.

y = 2x − 4

E.

y = 5x + 9

Multiple Select

Ms. Henderson gave her students a list of functions. Which functions have the same zeros? Select TWO correct answers.

• $$y=x^2−4x+4​$$

• $$y=x+2$$

• $$y=−4x+3​$$

• $$y=2^x−4​$$

• $$y=5x+9$$

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Which graph has two positive zeros and a negative y-intercept?

B

C

A

Multiple Choice

Which graph has two positive zeros and a negative y-intercept?

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Which coordinates represent the intercepts of the
function on the graph?

A.

(6, 0) and (0, –6)

B.

(6, 0) and (–6, 0)

C.

(0, 6) and (0, –6)

D.

(0, 6) and (–6, 0)

Multiple Choice

Which coordinates represent the intercepts of the function on the graph?

• (6, 0) and (0, –6)

• (6, 0) and (–6, 0)

• (0, 6) and (0, –6)

• (0, 6) and (–6, 0)

Essential Question Debrief

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How can you
identify the
x-intercepts,
zeros, and
y-intercepts of a
function?

I can identify the x-intercepts, zeros,
and y-intercepts of a function by…

35

DOL: Given a set of
problems, students
will correctly identify
the x-intercepts,
y-intercepts, and
zeros in
mathematical and
real-world problems
using the graph of
linear, quadratic,
and exponential
functions on the
coordinate plane in
at least 4 of 5
questions.

Demonstration of Learning

Learner Slides

Learner Slides

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The point where a function crosses the y-axis is called the y-intercept. When
looking at a real-world problem, the y-intercept is the initial value.

y-intercept

Circle all the points that

are on the y-axis.

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Alonso graphed a linear function. Which ordered pair
best represents the location of the y-intercept?

A.

B.

(0, −2)

C.

D.

( −2, 0)

Practice

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Jennifer graphed the function on the graph below. What
are the coordinates of the y-intercept of the graph?

Practice

(0, 5)

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Mr. Li presented his students a function with a y-intercept of 4. Which graph
represents the function Mr. Li showed his students?

A

B

C

D

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The point where a function crosses the x-axis is called the x-intercept or the
zero of the function.

x-intercepts

zeros

Circle all the points that

are on the x-axis.

42

Rebecca graphed a linear function. What is the zero of
the function?

A.

(−6, 0)

B.

(0, 2)

C.

(2, 0)

D.

(0, −6)

Practice

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Mr. Amos gave his students the graph of a quadratic
function. What are the x-intercepts of the function? Select
TWO that apply.

A.

x = 4

B.

x = −2

C.

x = −4

D.

x = 0

E.

x = 8

Practice

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Simone graphed a function with an x-intercept of −3. Which graph represents the
function Simone graphed?

A

B

C

D

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We can use a graphing calculator to help us determine the zeros and
y-intercepts of functions. When using Desmos, the calculator will mark the
intercepts on the function. All you will need to do is hover over the point to get
the coordinates.

Lillie used her calculator to
graph the function y = 2x – 5.
Identify the x and y-intercept
of the function.

y-intercept: _______________

x-intercept: _______________
(2.322, 0)

(0, −4)

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Alexander has the following function graphed on his
homework. What are the x-intercept and the y-intercept
of the line?

Practice

A.

x-intercept: (8, 0)
y-intercept: (0, 2)

B.

x-intercept: (−2, 0)
y-intercept: (0, 4)

C.

x-intercept: (−2, 0)
y-intercept: (0, 8)

D.

x-intercept: (4, 0)
y-intercept: (0, 8)

All listed images generated using Adobe Illustrator unless otherwise
noted.

Citations