Math9 Wk9.docx

Created by: GREG M, Et al
DAILY LESSON LOG
School: Grade Level: 9
Teacher: Learning Area: Mathematics
Teaching Dates & Time: Week 9 Quarter: 1st
Quarter
MONDAY TUESDAY WEDNESDAY THURSDAY FRIDAY
I. OBJECTIVES
A. Content Standards demonstrates understanding
of key concepts of quadratic
equations, inequalities and
functions, and rational
algebraic equations.
demonstrates
understanding of key
concepts of quadratic
demonstrates understanding
of key concepts of quadratic
demonstrates
understanding of key
concepts of quadratic
ICL
B. Performance
Standards
is able to investigate
thoroughly mathematical
relationships in various
situations, formulate real-life
problems involving quadratic
inequalities and functions,
and rational algebraic
equations and solve them
using a variety of strategies.
problems involving
quadratic inequalities and
algebraic equations and
solve them using a variety of
strategies.
inequalities and functions, and
rational algebraic equations and
strategies.
problems involving
quadratic inequalities and
algebraic equations and
strategies.
C. Learning
Competencies/
Objectives
( Write the Lode for
each)
determines the equation of a
quadratic function given:
(a) a table of values;
(b) graph;
(c) zeros
determines the equation of a
quadratic function given: (a)
a table of values;
(b) graph;
(c) zeros.
solves problems involving
quadratic functions.
solves problems involving
II.CONTENT
( Subject Matter)
Determining the equation of a
quadratic function given a
table of values, a graph, or
the zeros
Determining the equation of
a quadratic function given a
the zeros
Solving problems involving
Solving problems involving
III. LEARNING
RESOURCES
A. References
1. Teacher’s Guide
pages
Pages 30-35 Pages 30-35 Pages 40-45 Pages 50-55
2. Learner’s Material
pages
Pages 50-55 Pages 50-55 Pages 60-65 Pages 80-85
3. Textbook pages Chapter 4, Sections 3-4 Chapter 4, Sections 3-4 Chapter 5, Sections 1-2 Chapter 5, Sections 3-4
4. Additional Materials
from Learning
Resource LR portal
Graph paper, markers Graph paper, markers Graph paper, markers Graph paper, markers, real-
world problem scenarios.
B. Other Learning
Resources
Online graphing tools (if
available)
Online graphing tools (if
available)
Online problem-solving tools (if
available)
Online problem-solving tools
(if available).
IV. PROCEDURE

A. Reviewing previous
Lesson or presenting
new lesson
Teacher: "Let's begin by
reviewing what we learned in
the previous lesson. Can
someone remind us of the
effects of changing the values
of a, h, and k on the graph of
a quadratic function?"
Student response: (Students
summarize the effects, such
as vertical
stretch/compression for 'a',
horizontal shift/translation for
'h', and vertical
shift/translation for 'k'.)
Teacher: "Great job! Today,
we will apply our
understanding of quadratic
functions to determine their
equations given different
representations. Let's get
started!"
briefly reviewing what we
covered in our previous
lesson. Can someone
explain how to determine the
equation of a quadratic
function given a table of
values?"
summarize the process,
such as substituting values
from the table into the
general form of the quadratic
function and solving for the
coefficients.)
Teacher: "Well done! Today,
we will continue our
exploration by focusing on
determining the equation of
a quadratic function using a
different representation.
Let's proceed."
Teacher: "Let's begin by briefly
reviewing what we learned in
our previous lesson about
quadratic functions. Can
someone explain what a
quadratic function is?"
provide a definition, such as a
function of the form f(x) = ax^2
+ bx + c.)
Teacher: "Great! Today, we will
focus on applying quadratic
functions to solve real-world
problems. This skill will help us
analyze and make predictions
in various situations. Let's get
started."
briefly reviewing the
problem-solving techniques
we discussed in the previous
lesson. Can someone
explain the steps involved in
solving problems with
quadratic functions?"
summarize the process,
such as identifying the given
information, representing the
situation using a quadratic
function, and applying
algebraic techniques to find
the solutions.)
Teacher: "Great! Today, we
will continue our exploration
of problem-solving with
quadratic functions. We will
focus on more complex
scenarios and challenges.
Let's dive into the lesson."
B. Establishing a purpose
for the lesson
Teacher: "Today, our
objective is to learn how to
determine the equation of a
quadratic function using a
the zeros. By the end of the
lesson, you will be able to find
the equation of a quadratic
function given these different
representations. This skill will
be valuable in analyzing and
solving real-world problems
involving quadratic functions."
objective is to further
develop our skills in
graph. By the end of the
lesson, you will be able to
analyze a graph and find the
equation of the
corresponding quadratic
function. This will allow us to
model and solve real-world
problems more effectively."
Teacher: "Today, our objective
is to develop our problem-
solving skills using quadratic
functions. By the end of the
lesson, you will be able to apply
quadratic functions to solve
real-world problems. This ability
will allow us to model and make
predictions in scenarios that
involve quadratic
relationships."
objective is to further
enhance our problem-
solving skills using quadratic
functions. We will tackle
more challenging real-world
problems and practice
critical thinking to analyze
and model complex
situations. By the end of the
lesson, you will be able to
apply quadratic functions to
solve a variety of problems."
C. Presenting examples/
instances of the new
lesson.
Teacher: "To begin, let's look
at some examples of
determining the equation of a
quadratic function using
different representations. I will
present a table of values, a
graph, and the zeros, and we
will work through the process
together."
Teacher: "To start, let's
examine some examples
where we are given a graph
of a quadratic function and
need to determine its
equation. I will present
different graphs, and we will
work through the process
together."
Teacher: "To begin, I will
present several real-world
problems that can be solved
using quadratic functions. We
will work through the examples
together, discussing the steps
and strategies involved."
Teacher: "To start, I will
present several real-world
problems that involve
quadratic functions but
require additional steps or
strategies to solve. We will
work through the examples
together, discussing the

approaches and techniques
involved."
D. Discussing new
concepts and practicing
new skills. #1
Teacher: "Let's start with
quadratic function using a
table of values. Can someone
explain the process to the
class?"
explain that they can
substitute the x and y values
from the table into the general
form of the quadratic function,
y = ax² + bx + c, to form a
system of equations.)
Teacher: "Exactly! By
substituting the values from
the table into the equation,
we can form a system of
equations and solve for the
coefficients a, b, and c. Let's
practice this process
together."
Teacher: "When determining
the equation of a quadratic
function from a graph, what
key points or features do we
need to identify?"
mention the vertex, axis of
symmetry, and one
additional point on the
graph.)
Teacher: "Exactly! By
identifying the vertex and
another point, we can
determine the values of a, h,
and k and write the equation
of the quadratic function.
Let's practice this process
together."
Teacher: "When solving
functions, what key steps
should we follow?"
mention identifying the given
information, representing the
situation using a quadratic
function, and using algebraic
techniques to solve the
equation.)
Teacher: "Exactly! To solve
functions, we need to analyze
the given information, form a
quadratic equation or function,
and use appropriate techniques
to find the solutions. Let's
practice this process together."
Teacher: "When facing more
complex problems, what
additional considerations or
techniques should we keep
in mind?"
mention strategies such as
factoring, completing the
square, or using the
quadratic formula.)
Teacher: "Exactly! In some
cases, factoring, completing
the square, or using the
quadratic formula may be
necessary to find the
solutions. Let's practice
applying these techniques to
solve more challenging
problems together."
E. Discussing new
concepts and practicing
new skills #2.
Teacher: "Next, let's move on
to determining the equation of
graph. Can someone share
their understanding of this
process?"
explain that they can use the
vertex form of the quadratic
function, y = a(x - h)² + k, to
identify the values of a, h, and
k from the graph.)
Teacher: "Well done! By
analyzing the graph and
identifying the vertex and one
other point, we can determine
the values of a, h, and k and
write the equation of the
quadratic function. Let's work
through some examples
together."
Teacher: "Now, let's move
on to determining the
function using the zeros.
Can someone share their
understanding of this
process?"
explain that if the zeros or
roots of the quadratic
function are given, they can
be used to determine the
factors and write the
equation.)
Teacher: "Well explained! By
using the zeros, we can
determine the factors of the
quadratic function and write
its equation. Let's work on
some examples together."
Teacher: "In some situations,
the problem may not directly
provide a quadratic function.
Instead, we may need to
analyze the problem and
formulate the quadratic
equation ourselves. Can
anyone provide an example?"
provide an example, such as
determining the height of a
projectile based on its initial
velocity and angle.)
Teacher: "Well done! In such
cases, we need to understand
the problem, identify relevant
variables, and create a
quadratic equation that models
the situation accurately. Let's
practice this process together."
Teacher: "In real-world
scenarios, we often
encounter situations where
quadratic functions need to
be combined with other
mathematical concepts or
models. Can anyone think of
an example?"
provide an example, such as
using quadratic functions to
optimize a problem involving
area or revenue.)
Teacher: "Excellent! In such
cases, we need to integrate
quadratic functions with
other mathematical ideas or
models to solve the problem
effectively. Let's practice this
process together."
F. Developing Mastery Teacher: "Now, let's practice
Teacher: "Now it's time for
hands-on practice. In pairs
Teacher: "Now, it's time for
independent or group practice. I
Teacher: "Now, it's time for
independent or group

(Lead to Formative
Assessment 3)
quadratic function using
different representations. In
pairs or small groups, you will
be given several examples
involving tables of values,
graphs, or zeros. Analyze the
given information and use the
appropriate method to find
the equation of each
quadratic function. Discuss
your findings with your group
members and be prepared to
share your solutions with the
class."
or small groups, you will be
given several graphs and
zeros of quadratic functions.
Analyze the given
information and determine
the equation of each
quadratic function using the
appropriate method. Discuss
your findings with your group
members and be prepared
to share your solutions with
the class."
will provide you with a set of
real-world problems that can be
solved using quadratic
functions. Analyze the
problems, apply the appropriate
strategies, and solve for the
desired quantities. Work
individually or in pairs, and feel
free to ask questions if you
need clarification."
practice. I will provide you
with a set of more complex
real-world problems that
involve quadratic functions.
Analyze the problems,
determine the appropriate
techniques to apply, and
solve for the desired
quantities. Work individually
or in pairs, and feel free to
ask questions if you need
clarification."
G. Finding practical
application of concepts
and skills in daily living
Teacher: "Quadratic functions
are often used to model real-
world situations. In pairs or
small groups, brainstorm and
discuss different scenarios
where quadratic functions can
be applied. Think about how
quadratic function can help
solve problems in those
situations. Share your ideas
with the class."
Teacher: "Quadratic
functions can be used to
model various real-world
situations. In pairs or small
groups, brainstorm and
discuss different scenarios
where quadratic functions
can be applied. Think about
how determining the
function, given different
representations, can help
solve problems in those
situations. Share your ideas
with the class."
Teacher: "Quadratic functions
have practical applications in
various fields, such as physics,
engineering, and economics. In
pairs or small groups, discuss
and share examples of real-
world situations where
quadratic functions can be used
to solve problems or make
predictions. Present your
findings to the class."
Teacher: "Quadratic
functions have diverse
applications in different
fields. In pairs or small
groups, research and
present examples of real-
world problems or scenarios
where quadratic functions
are used to solve complex
problems or make
predictions. Discuss the
challenges and potential
implications of these
applications."
H. Making Generalizations
and Abstraction about
the Lesson.
Teacher: "Based on our
discussions and practice, let's
make some generalizations
about determining the
function given different
representations. Can anyone
provide a general statement
or rule that applies to all
cases?"
provide generalizations, such
as the need for at least three
points from a table of values,
the ability to identify the
vertex and one additional
point from a graph, and using
discussions and practice,
let's make some
generalizations about
a quadratic function given
different representations.
Can anyone provide a
general statement or rule
that applies to all cases?"
provide generalizations,
such as the need to identify
the vertex and one additional
point from a graph and using
the zeros to determine the
discussions and problem-
solving practice, let's make
some generalizations about
solving problems involving
quadratic functions. Can
anyone provide a general
statement or rule that applies to
all cases?"
provide generalizations, such
as the need to identify the given
information, model the situation
using a quadratic function, and
apply algebraic techniques to
find the solutions.)
problem-solving practice and
discussions, let's make
some generalizations about
solving complex problems
involving quadratic functions.
Can anyone provide a
general statement or rule
that applies to these
cases?"
provide generalizations,
such as the need to apply
advanced techniques like
factoring, completing the
square, or using the
quadratic formula when

the zeros to determine the
equation.)
Teacher: "Excellent! These
generalizations will guide us
in finding the equations of
quadratic functions accurately
and efficiently."
equation.)
Teacher: "Fantastic! These
generalizations will guide us
in determining the equations
of quadratic functions
accurately and efficiently."
Teacher: "Excellent! These
generalizations will guide us in
solving problems involving
quadratic functions effectively
and efficiently."
faced with complex
problems.)
Teacher: "Wonderful! These
generalizations will help us
approach complex problem-
solving tasks involving
quadratic functions with
confidence and skill."
I. Evaluating Learning Question 1: Given that the
quadratic function has zeros
at x = 2 and x = -3, determine
its equation.
A) y = (x - 2)(x + 3)
B) y = (x + 2)(x - 3)
C) y = (x - 2)(x - 3)
D) y = (x + 2)(x + 3)
Please choose the correct
option (A, B, C, or D) that
represents the equation of the
quadratic function based on
the given zeros.
Question 2: Given the graph
of a quadratic function:
-
Question 1: Given the
following table of values for
a quadratic function:
x y
-2 6
-1 2
0 1
1 2
2 6
Determine the equation of
the quadratic function.
A) y = x^2 - 2x + 1
B) y = -x^2 + 2x + 1
C) y = -x^2 - 2x + 1
D) y = x^2 + 2x + 1
represents the equation of
the quadratic function based
on the given table of values.
Determine the equation of
the quadratic function.
A) y = x^2
B) y = -x^2
Question: A farmer wants to
build a rectangular pen for their
animals using a riverbank as
one side. The farmer has 200
meters of fencing material to
enclose the other three sides.
What dimensions should the
farmer choose to maximize the
area of the pen?
A) Length: 50 meters,
Width: 50 meters
B) Length: 75 meters,
Width: 25 meters
C) Length: 100 meters,
Width: 50 meters
D) Length: 150 meters,
Width: 25 meters
represents the dimensions of
the rectangular pen that
maximize its area based on the
given problem involving a
quadratic function.
Question: A ball is thrown from
the ground with an initial
velocity of 25 m/s at an angle of
30 degrees above the
horizontal. The height of the ball
above the ground after t
seconds is given by the
equation h = -4.9t^2 + 25t. How
Question 1: A ball is thrown
upward from the ground with
an initial velocity of 30 m/s.
The height of the ball above
the ground after t seconds is
given by the equation h = -
5t^2 + 30t. How long does it
take for the ball to reach the
highest point?
A) 3 seconds
B) 5 seconds
C) 6 seconds
D) 10 seconds
represents the time it takes
for the ball to reach the
highest point based on the
given quadratic function.
Question 2: A rectangular
garden has an area of 48
square meters. The length of
the garden is 2 meters
longer than its width. What
are the dimensions of the
garden?
A) Length: 6 meters,
Width: 4 meters
B) Length: 8 meters,
Width: 6 meters
C) Length: 10 meters,
Width: 8 meters
D) Length: 12 meters,

Determine the equation of the
quadratic function.
A) y = x^2 + 2x + 1
B) y = -x^2 - 2x - 1
C) y = -x^2 + 2x - 1
D) y = x^2 - 2x + 1
the given graph.
Question 3: Given the
following table of values for a
quadratic function:
x y
-1 5
0 1
1 -1
Determine the equation of the
quadratic function.
A) y = x^2 + 2x + 1
B) y = -x^2 - 2x - 1
C) y = -x^2 + 2x - 1
D) y = x^2 - 2x + 1
the given table of values.
C) y = x^2 + 1
D) y = -x^2 + 1
on the given graph.
Question 3: Given that the
quadratic function has zeros
at x = -1 and x = 4,
determine its equation.
A) y = (x + 1)(x - 4)
B) y = (x - 1)(x + 4)
C) y = (x - 1)(x - 4)
D) y = (x + 1)(x + 4)
on the given zeros.
long does it take for the ball to
reach the maximum height?
A) 2 seconds
B) 2.55 seconds
C) 2.86 seconds
D) 3 seconds
represents the time it takes for
the ball to reach the maximum
height based on the given
quadratic function.
Question: A water fountain
shoots water into the air,
forming a parabolic shape. The
height of the water above the
ground at time t seconds is
given by the equation h = -2t^2
+ 8t + 3. At what time does the
water hit the ground?
A) 1 second
B) 2 seconds
C) 3 seconds
D) 4 seconds
represents the time at which the
water hits the ground based on
the given quadratic function.
Width: 10 meters
represents the dimensions of
the rectangular garden
based on the given quadratic
function.
Question 3: A company
manufactures and sells x
units of a product. The total
cost (in dollars) to produce
the units is given by the
function C(x) = 2x^2 + 10x +
100. The revenue (in dollars)
generated from selling x
units is given by the function
R(x) = 30x. Find the number
of units the company needs
to sell in order to break even
(i.e., when revenue equals
cost).
A) 5 units
B) 10 units
C) 15 units
D) 20 units
represents the number of
units the company needs to
sell in order to break even
based on the given quadratic
functions.
J. Additional Activities for
Application or
Remediation
Teacher: "For students who
would like additional practice
or need remediation, I have
prepared an optional
individual activity where you
will be given a set of graphs
and zeros of quadratic
functions. Your task is to
determine the equation of
each quadratic function
using the appropriate
would like additional practice or
need remediation, I have
prepared an optional individual
activity where you will be given
a set of word problems that can
be solved using quadratic
functions. Your task is to
analyze the problems, form
appropriate equations, and
solve for the desired quantities.
would like additional practice
or need remediation, I have
prepared an optional
individual activity where you
will be given a set of
complex word problems that
require advanced problem-
solving techniques with
quadratic functions. Your
task is to analyze the

method. This will help you
reinforce your understanding
of the process. If you're
interested, please let me
know, and I will provide you
with the activity handout.
Keep up the fantastic effort!"
This will help you reinforce your
problem-solving skills. If you're
interested, please let me know,
and I will provide you with the
activity handout. Keep up the
fantastic effort!"
problems, determine the
appropriate approaches, and
solve for the desired
quantities. This will help you
further enhance your
problem-solving skills. If
you're interested, please let
me know, and I will provide
you with the activity handout.
Keep up the fantastic effort!"
V. REMARKS
VI. REFLECTION
A. No. of learners earned
80%in the evaluation.
B. No. of learners who
required additional
activities for remediation
who scored below 80%
C. Did the remedial lesson
work? No. of learners who
have caught up with the
lesson.
D. No. of learner who
continue to require
remediation
E. Which of my teaching
strategies worked well?
Why did these work?
F. What difficulties did I
encounter which my
principal or supervisor can
help me solve?
G. What innovation or
localized materials did I
used/discover which I wish
to share with other
teachers?
Prepared by:
Checked by:
Teacher III
School Principal I

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