DAILY
LESSON
LOG
Annex to DepEd Order 42,
s.2016
School
Grade
TEN (10)
Level:
Learning Area:
MATHEMATICS
Quarter:
3rd Grading
FR. GRATIAN MURRAY, AFSC INTEGRATED SCHOOL
Teacher
Teaching Dates & Time
I. OBJECTIVES
1. Content Standards
2. Performance Standards
3. Learning Competencies
Objectives
BEVERLY N. ALON
March, 2023
The learner demonstrates understanding of key concepts of
polynomial function.
The learner is able to conduct systematically a mathematical
investigation involving polynomial functions in different fields.
Graphs polynomial functions. (M10AL-Ia-b-1)
a. Sketch the graph of polynomial function.
a. Value accumulated knowledge as means of new
understanding.
Graphs of Polynomial Functions
II. CONTENT
III. LEARNING RESOURCES
A. References
pp. 93-105
1. Teacher’s Guide
pp. 112-121
2. Learner’s Materials
3. Textbook
4. Additional Materials from Learning
Resources (LR) portal
B. Other Learning Resources
IV. PROCEDURES
A. Reviewing previous lesson or
presenting the new lesson
B. Establishing a purpose for the
lesson
Polynomial Dance
Describe the behavior of each polynomial function through different
dance moves.
1. 𝑦 = 𝑥3 + 3𝑥2 – 𝑥 − 3
2. 𝑦 = (2𝑥 + 3) (𝑥 − 1) (𝑥 − 4)
Think-Pair-Share
Find the x- and y- intercepts of the polynomial function
𝑃(𝑥)=(𝑥+1)2 (𝑥+2) (𝑥−2) (𝑥−3)
1. Sketch the graph of the polynomial using the result.
2. In graphing the polynomial, where did you find difficulties?
3. Are the intercepts enough information to sketch the graph?
C. Presenting examples/Instances
of the new lesson
The polynomial in factored form is 𝑦=(𝑥−1)(𝑥+1)(𝑥−2)(𝑥+2)
The roots(x-intercepts) are 1,−1,2 and −2
The y-intercept is 4 There are no roots of even multiplicity
𝑎n=1,
𝑎n>0,
𝑛=4 and is even Since 𝑛 is even and 𝑎n>0, then the graph
comes down from the extreme left and goes up to the extreme right.
There are 3 turning points.
The graph will follow the pattern:
Describe or determine the following, then sketch the graph of
y = -x3 – x2 + x + 1
a. leading term
b. behavior of the graph
c. x-intercepts
d. multiplicity of roots
e. y-intercept
f. number of turning points
g. sketch
Solution:
𝑦=−𝑥3 −𝑥2 + 𝑥 + 1
a. leading term: -1
b. behavior of the
graph: the graph
comes down from the extreme left and goes down to the
extreme right
( 𝑛 is odd and 𝑎n<0)
a. x-intercepts:
−1,−1 and 1
the polynomial in
factored form is
𝑦=−(𝑥+1)2(𝑥−1)
b. multiplicity of
roots:
-1 is of even
multiplicity 2,
therefore the graph is
tangent to the x-axis
at (−1,0)
e. y-intercept: 1
f. number of turning
points: 2
(for the graph to
intersect the
computed
x-intercept and
y-intercept, and a
tangent to (−1,0)
there should be 2
turning points)
g. sketch:
D. Discussing new concepts and
practicing new skills # 1
1. How do you find the activity?
2. What are the things to identify to sketch the graph of polynomial
functions?
3. How do we sketch the graph of polynomial functions?
E. Discussing new concepts and
practicing new skills # 2
Sketch the graph of
P(x) = 2x3 – 7x2 – 7x+ 12
a. leading term: ___________________
b. behavior of the graph: _____________
( 𝑛 is odd and 𝑎𝑛>0)
c. x-intercepts: __________________
d. multiplicity of roots:_____________
e. y-intercept:___________
f. number of turning points: 2
g. sketch:
F. Developing mastery (leads to
Formative Assessment 3)
G. Finding practical application of
concepts and skills in daily living
Sketch the graph of the polynomial function
𝑦=(𝑥+2)2 (𝑥−3) (𝑥+1)
Sketch the graph of the polynomial function
𝑦 = −(x + 2)(x + 1)2
(x − 3)
H. Making generalizations and
abstractions about the lesson
To sketch the graph of a polynomial function we need to
consider the following:
a. leading term
b. behavior of the graph
c. x-intercepts
d. multiplicity of roots
e. y-intercept
f. number of turning points
I. Evaluating learning
Sketch the graph of the polynomial function
y = x6 + 4x5 + 4x4 – 2x3 – 5x2 – 2x
J. Additional activities for
application or remediation
1. Follow Up
Sketch the graph of: y = x4 and y = x5
2. Study
Applying the concepts of polynomial functions in
answering real life problems
G10 Mathematics LM pages 122 – 123
Prepared by:
BEVERLY N. ALON
Teacher I
Checked by:
RICARDO CAMINIAN
Head Teacher 1