School Calbayog City National High School Grade Level 9

GRADES 9 Teacher Rochele A. Santiago Learning Area MATHEMATICS

DAILY LESSON LOG
Teaching Dates and Time September 2 – 6, 2019 Quarter SECOND
September 2, 2019 September 3, 2019 September 4, 2019 September 5, 2019
Teaching Day and Time
8:15-9:15 am (Tuesday) 8:15-9:15 am (Wednesday) 8:15-9:15 am (Thursday) 8:15-9:15 am (Friday)
Grade Level Section

Session 1 Session 2 Session 3 Session 4

I. OBJECTIVES

1. Content Standards The learner demonstrates understanding of key concepts of quadratic equations, inequalities and functions, and rational algebraic equations.
2. Performance The learner is able to investigate thoroughly mathematical relationships in various situations, formulate real-life problems involving quadratic equations, inequalities
Standards and functions, and rational algebraic equations and solve them using a variety of strategies.
3. Learning Determines the equation of a Determines the equation of a Determines the equation of a Solves problems involving quadratic
Competencies/ quadratic function given: (a) a table of quadratic function given: (a) a quadratic function given: (a) a functions.
Objectives values; (b) graph; (c) zeros. table of values; (b) graph; (c) table of values; (b) graph; (c) (M9AL-Ii-j-2)
(M9AL-Ij-1) zeros. zeros.
(M9AL-Ij-1) (M9AL-Ij-1) a. Identify the solution of quadratic
a. Find the roots of a function
quadratic function a. Determine the equation of a a. Determine the equation of b. Solve problems involving quadratic
b. Determine the equation of a a quadratic function given
quadratic function given its function
quadratic function given its zeros its graph
c. Value accumulated table of values c. Apply concepts learned in solving
b. Value accumulated problems involving quadratic
knowledge as means of b. Value accumulated knowledge
knowledge as means of
new understanding as means of new understanding new understanding function

II. CONTENT Finding the Equation of a Quadratic Finding the Equation of a Quadratic Finding the Equation of a Quadratic
Applications of Quadratic Functions
Function Function Function
III. LEARNING RESOURCES

A. References

1. Teacher’s Guide
pp.104-109 pp.104-109 pp.104-109 pp.110-115
 2. Learner’s
Materials pp.156-173 pp.156-173 pp.156-173 pp.174-183

3. Textbook

4. Additional Materials
from Learning
Resource (LR)
portal

B. Other Learning Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite Grade 9 LCTG by DepEd Cavite
Resources Mathematics 2016, Mathematics 2016, Mathematics 2016, Mathematics 2016,
activity sheets, laptop and monitor activity sheets, laptop and monitor activity sheets, laptop and monitor activity sheets, laptop and monitor
IV. PROCEDURES

A. Reviewing previous Give Me My Roots! Preliminary Activity! What Are My Zeros? Direction: Solve the problem by following
lesson or presenting the Direction: Given a quadratic function y = The table of values below describes a Direction: Examine the graph of the the given steps.
new lesson x2 – 3x + 2, find the roots using the quadratic function. Find the equation quadratic function y = x2 – 2x – 3.
following methods: of the quadratic function by following
1. by factoring the given procedure. If the perimeter of the rectangle is
2. by using the quadratic formula x -3 -1 1 2 3 100 m, find its dimensions if its area is a
3. by completing the square y -29 -5 3 1 -5 maximum. Complete the table below for the
Based on the quadratic function given on 1. Substitute three (3) ordered pairs possible dimensions of the rectangle and
the activity, how can you say that the (x,y) in their corresponding areas. W stands for
obtained value of x is the root of the y = x2 y = ax2 + bx + c width, L stands for length, and A stands for
– 3x + 2? 2. What are the three equations you area. The first column has been completed
1. How is obtained roots related to come up with?____,_____,_____ for you.
zeros of a function? 3. Solve for the values of a, b and c. Follow-up Questions:
4. Write the equation of the quadratic 1. How would you describe the
function graph?
2
y = ax + bx + c. 2. Give the vertex of the parabola
Follow-up Questions: and its axis of symmetry. Follow-up Questions:
1. How did you obtain the three 3. At what values of x does the graph 1. What is the largest area that you
equations? intersect the obtained?
2. What do you call the three x -axis? 2. What are the dimensions of a rectangle
equations? 4. What do you call these with the largest area?
3. What perimeter of the given rectangle is
x -coordinates where the curve
100. Make a mathematical statement
crosses the for the perimeter.
x-axis? 4. Simplify the obtained equation and
5. What is the value of y at these solve for the length of the rectangle in
values of x? terms of its width.
5. Express the area of a rectangle as a
 function of its width.
6. What kind of equation is the result?

B. Establishing a purpose a. Find the roots of a a. Determine the equation of a a. Determine the equation of a. Identify the solution of quadratic
for the lesson quadratic function quadratic function given its table of a quadratic function given function
b. Determine the equation of a values its graph b. Solve problems involving quadratic
quadratic function given its zeros
function
C. Presenting examples/ What’s My Rule? Illustrative Example. Determine the When the vertex and any point on the For deeper understanding of the
instances of the Direction: Work in groups of three (3) equation of the quadratic function parabola are clearly seen, the application of quadratic function in real-life
lesson members each. Perform this activity. represented by the table of values equation of the quadratic function can provide the learners with an example.
below. easily be determined by using the
The table below corresponds to a form of a quadratic function y = a (x –
quadratic function. Examine it. h)2 + k. Marvin has a mango plantation. If he
x -3 -2 -1 0 1 2 3
x -3 -1 1 2 3 y 24 16 10 6 4 4 6 picks the mangoes now, he will get 40
y -29 -5 3 1 -5 Solution: Example: small crates and make a profit of 100
Task: Notice that you cannot find any Find the equation of the quadratic pesos per crate. For every week that he
1. Plot the points and study the graph. zeros from the given table of values. function determined from the graph delays picking, her harvest increases by 5
What have you observed? In this case, take any three ordered below. crates, but the selling price decreases by
2. What are the zeros of the quadratic pairs from the table, and use these as 10 pesos per crate. When should Marvin
function? How can you identify them? the values of x and y in the equation harvest his mangoes for him to have a
2
3. If the zeroes are r1 and r2, express the y = ax + bx + c. Let’s say
maximum profit?
equation of the quadratic function
using f(x) = a(x– r1)(x – r2), where a is using point (1,4) The table shows the possible number of
any nonzero constant. 4 = a(1) 2
+ b(1) + c crates that Marvin harvested and his profit
4. What is the quadratic equation that 4 = a + b + c equation 1 within the indicated week.
corresponds to the table?
Legend:
using point (-1,10)
Number of weeks waiting (w)
10 = a(-1)2 + b(-1) + c
10 = a – b + c equation 2 Number of crates (c)
Solution: Profit per crate (P)
using point (2, 4) The vertex of the graph of the Total profit (T)
4 = a(2)2 + b(2) + c quadratic function is (2, -3). The graph
4 = 4a + 2b + c equation 3 passes through points (5, 0). By
replacing x and y with 5 and 0,
respectively, and h and k with 2 and
We obtain system of 3 equations a, b, -3, respectively, we have
and c.
y = a(x – h)2 + k
Using eq.1 and eq.2 0 = a(5 – 2)2 + (-3)
The graph of the given function is shown
4=a+b+c 0 = a(3)2 – 3
3 = 9a below.
+ 10 = a – b + c
we have 14 = 2a + 2c
a=
 equation 4

Multiply the terms in the eq. 2 by 2 Thus, the quadratic

and add corresponding terms in eq. 3
to eliminate b. equation is y =

Using 2(eq.2) and eq.3

or y =
20 = 2a – 2b + 2c
+ 4 = 4a + 2b + c
we have 24 = 6a + 3c The blue line shows the number of crates
equation 5
Notice that equation 4 and 5 harvested per week and the orange line
constitute a system of linear shows the profit earned per crate.
equations in two variables. To solve
for c, multiply the terms in equation 4 To obtain the total profit, multiply the
by 3 and subtract corresponding number of crates by the profit per crate.
terms in equation 5.
Using 3(eq.4) and eq.5
Formulating the equation we will arrive at
42 = 6a + 6c
- 24 = 6a + 3c P = (40 + 5x)(100 – 10x)
18 = 3c P = -50x2 + 100x + 4000
c=6
by substitution using eq.4 and the
value of c, solve for a Therefore, according to the table and graph
14 = 2a + 2(6) shown, Marvin should harvest his mangoes
14 = 2a + 12 during the 1st week so that he will have his
2a = 14 – 12 maximum profit.
a=1
by substitution using eq.1 and the
value of c and a, solve for b
4=a+b+c
4=1+b+6
4=7+b
b=4–7
b = -3
Thus, a = 1, b = -3, and
c = 6. Substitute it in the quadratic
function, the equation is f(x) = x2 – 3x
+ 6.
D. Discussing new concepts Find my Equation! Derive My Equation! Pattern from Curve! Direction: Analyze and solve the problem.
and practicing new skills Work in pairs. Determine the equation The company of Cherry Mobile
#1 Find a quadratic function whose zeros are of the quadratic function represented Work with your partner. Study the cellular phones can sell 200 units per
-1 and 4. by the table of values. graph and determine the equation of month at 2,000 pesos each. Then they
the quadratic function. found out that they can sell 50 more cell
Solution:
 If the zeros are -1 and 4, then x = -1 or x = phone units every month for each 100
4. It follows that x + 1 = 0 or x – 4 = 0, pesos decrease in price.
then (x + 1) (x – 4) = 0
x2 – 3x – 4 = 0

The equation of the quadratic function

f(x) = x2 – 3x – 4 is not unique since there
are other quadratic functions whose zeros
are -1 and 4. These equations of Follow – up questions:
quadratic functions is obtained by 1. What is the opening of the
multiplying the right hand side of the parabola? What does it imply
equation by a nonzero constant. Thus, the regarding the value of a?
answer is f(x) = a(x2– 3x – 4) where a is a 2. Identify the coordinate of the
nonzero constant. vertex and any point on the
parabola.
3. Solve for the value of a by
substituting the coordinates of the
point that you have taken in place
of h and k respectively.
E. Discussing new Give my Equation! What method did you use to obtain Dare to Hit Me! Follow-up Questions:
concepts and Direction: Study the example below in the equation of the given quadratic Direction: Work with your partner to 1. How much is the sales amount if cell
practicing new skills finding the zeros of the quadratic function equation in the previous activity? solve the problem below. phone units are priced at 2,000 each?
#2 and try to reverse the process to find the Explain briefly how you obtained your 2. How much would be their sales if they
solution of the problem indicated in the answer. Mark plays golf every weekend at sell each phone unit at 1,600 pesos?
table on the right. Explain the procedure Riviera Golf Course, Silang Cavite. 3. Write an equation for the revenue
you have done to determine the equation The path of his golf ball follows a function.
of the quadratic function. trajectory. It hits the ground 400 4. What price per cell phone unit gives
meters away from the starting them the maximum monthly sales?
position. It just overshoots a tree, 5. How much is the maximum sale?
which is 20 m high and is 300 m away
from the starting point. From the given
information, find the equation
determined by the path of the golf ball

F. Developing mastery Direction: Find the equation of the Direction: Determine the equation of Direction: Solve for the given problem Direction: Solve for the given problem
(Leads to Formative quadratic function whose zeros are 2 + . the quadratic function represented by within the alloted time. following the same procedure as the
Assessment 3) . the table of values. previous problems given.
Show your solution. The vertex of the parabola is (-3,
Follow – up Questions: 5) and it is in the minimum point of the The ICT club of Calbayog City
1. Were you able to get the equation of graph. If the graph passes through the National High School celebrates their ICT
the quadratic function? point (-2, 7), what is the equation of month every year and in line with this, they
2. If no, what difficulties did you the quadratic function? have a film showing as a form of their fund
encounter? If yes, how did you raising. The ticket to a film showing costs
 manipulate the rational expression to 20 pesos. At this price the president of the
obtain the quadratic function? Explain club found out that all 300 seats are filled.
briefly. The president estimates that if the price is
3. What is the equation of the quadratic increased, the number of viewers will fall
function? by 50 for every 5 pesos increase.

Question:
1. What ticket price results in
greatest revenue?
d. At this price, what is the maximum
revenue?
G. Finding practical Match the Zeros! Derive My Equation! Profit or Loss! Angles Count!
applications of concepts Matching Type. Each quadratic function Direction: Form five groups. Analyze Direction: Work in groups of 5 members
and skills in daily living has a corresponding letter. Similarly, each Direction: Work with your partner and the graph and answer the questions each. Perform this mathematical
box with the zeros of the quadratic observe the pattern below and draw that follow. Have one representative investigation. Write your answer on a
function inside has a corresponding blank the 4th and 5th figures. Make a table of to explain the work to the class. manila paper.
below. Write the indicated letter of the values for the number of squares at
quadratic function on the corresponding the bottom and the total number unit Problem:
blank below the box containing the zeros squares, then find the resulting An angle is the union of two non-
of the function to get the hidden message. equation of the function. collinear rays. If there are 100 non-collinear
rays, how many angles are there? What
kind of function is represented by the
relationship? Given the number of rays,
how can you determine the number of
angles? How did you get the pattern or the
relationship?

Follow-up Questions:
1. Describe the graph
2. What is the vertex of the graph?
What does the vertex represent?
3. How many weeks should the
owner of the pineapple plantation
wait before harvesting the
pineapples to get the maximum
profit?
4. What is the equation of the
function?
H. Making generalizations A value of x that satisfies the quadratic To determine the equation of a To determine the equation of a Quadratic function can be applied in
and abstractions about function quadratic function given its table of quadratic function given its graph, different fields like physics, industry, and
the lesson f(x) = ax2 + bx + c are the zeros of the values, consider the following steps: perform the following steps: business and in various other mathematical
function since these are the values of x 1. Choose any three ordered pairs 1. Identify the coordinate of the problems. Familiarity with quadratic
when y equals 0. These zeros of the from the table and use these as vertex and any point on the graph. function, their zeros and their properties is
function can be determined by setting y to the values of x and y in the 2. Solve for the value of a by very important in solving real-life problems.
0 and solving the resulting equation equation substituting the coordinates of the
y = ax2 + bx + c. point that you have taken in place As with any other algebraic
 through different algebraic methods. 2. Apply systems of linear equation of h and k respectively. problems, we always represent all
in solving for the value of a, b and 3. Form the equation of a quadratic unknowns with the use of variables. We
c. function in the form y = a(x – h)2 + then construct a mathematical model that
3. Substitute the obtained value of a, k by substituting the obtained describes to the problem. We must always
b and c in the quadratic function. value of a and the x and y note what each of the variables pertain to,
coordinates of the vertex in h and to avoid confusion.
k respectively.
I. Evaluating learning Direction: Find one equation for each of Direction: Find the equation of the Direction: Give the equation of a Direction: Solve the problems. Show your
the quadratic function given its zeros. quadratic function shown by the table quadratic function whose graphs are complete solution.
1. 3, 2 ___________ of values. Show your complete describe below. 1. What are the dimensions of the largest
2. -2, 5 solution 1. The graph of f(x) = 3x2 shifted 4 rectangular field that can be enclosed
2 ___________ units downward with 60 m of wire?
2. The graph of f(x) = 4x2 shifted 2 2. Ian wants to fence a rectangular area
3. 1 + ,1 - __________ units to the left that has one side bordered by an
4. 3. The graph of f(x) = 3x2 shifted 5 irrigation. If he has 80 m of fencing
____________ units upward and 2 units to the materials, what are the dimensions and
5. 11 , 11 right the maximum area he can enclose?
3 3 ___________ 4. The graph of f(x) = -10x2 shifted 2
units downward and 6 units to the
left
J. Additional activities for Assignment: Assignment: Assignment: Assignment:
application or Study how to determine the equation Study how to determine the Have a research on the Study the concepts about direct
remediation of a quadratic function given its table equation of a quadratic function application of quadratic function variation.
of values. given its graph. in real-life and be ready to share
it to the class the next day. Reference:
Reference: Reference: Grade 9 Learning Module pp.194-205
Grade 9 Learning Module pp.161-162 Grade 9 Learning Module pp.161-162 Reference:
Websites (Google, Yahoo, Math-Aids.
Com)
V. REMARKS

VI. REFLECTION
a. No. of learners who earned
80% on the formative
assessment

b. No. of learners who require

additional activities for
remediation.

c. Did the remedial lessons

work? No. of learners who
have caught up with the
lesson.
d. No. of learners 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 use/discover
which I wish to share with
other teachers?