Lesson Plan in Mathematics for Grade 9
Janin R. Cosido
Teacher’s Name
Mati National Comprehensive High School
Name of School
Mangga Street, Barangay Sainz, Mati City, Davao Oriental
Address of School
I. Objectives
At the end of 60 minutes, the students will be able to:
a. determine the highest or lowest point (vertex), axis of symmetry, orientation or opening of the graph
b. draw the graph of a quadratic functions using the vertex, axis of symmetry, direction of the opening
of the graph, and given points
c. show creativity and neatness in sketching graphs
II. Subject Matter
Topic: Graphs of a Quadratic Functions (M9ALIg-h-i-1)
Concept: Parabola is the graph of a quadratic function.
In graphing quadratic functions, the following properties of the parabolas should be observed: vertex,
axis of symmetry, orientation/opening of the graph (upward or downward), x – intercept/s, y – intercept,
maximum / minimum point of the graph, domain and range of the function
Reference/s: Teacher’s Guide in Mathematics 9, pp. 97-98, pp. 100-102
Mathematics 9: Quarter 1-Module 6, Bryant et. al (2014), Oronce et. al
(2019), pp. 4-10
Mathematics 9 Learner’s Material, Bryant et. al (2014), pp. 140-155
Instructional Materials: PowerPoint Presentation, Visual-aids, Graphing
Board, Worksheet
Skill(s): Solving problems, sketching graphs, analysis
Value(s): cooperation, attentiveness, activeness
III. Procedure
 Classroom management
 Prayer
 Greetings
 Checking of attendance
 Classroom policies/rules
 Checking of homework/assignment
F. Review
Teacher’s Activity
Student’s Response
- Before we start our new lesson, let us review first of what we
have discussed last Friday.
Who can tell or share to the class about our last topic? Yes, Iza?
- Last meeting, we discussed about
Transforming Quadratic Function in
Standard Form into Vertex Form.
- Now, I’ll give you an example y = x2 - 2x - 3 and transform it
into the form y = a(x-h)2 + k. Solve it in your notebook and when
you’re done, share it to the class.
(After 3 minutes Crislyn raises her hand)
- What’s vertex form of the given quadratic function?
- The vertex is y = (x – 1)2 – 4
- That’s correct.
G. Motivation
Teacher’s Activity
Student’s Response
- I have here a motivational activity. In your group, think of a
number less than 20. Subtract this number from 20 and multiply
the difference by twice the original number.
What is the number that will give the largest product?
- The first group who will give the largest product will win the
game.
(The groups starts answering)
(After 3 minutes, group 4 raise their hands)
- Yes, group 4 what is the number that gives the largest product?
- Okay, correct.
- The number that gives the largest product
is 1 and the largest product is 361.
H. Presentation of the Topic (Lesson Proper)
Teacher’s Activity
a. Activities (Pre-define Instruction)
- Our lesson for today is about Graphs of Quadratic Function or
Graphing Quadratic Function.
Student’s Response
- The graph of a quadratic function is called parabola as what
you can see in the illustration. That is a parabola.
- We can also see some illustrations or images of parabola in reallife like gateways, bridges, and the logo of McDonald’s. These are
some examples of real-life illustrations of parabola.
Illustrations:
(The students will analyse the pictures)
- Now, how to sketch the graph of a quadratic function? The
following properties of the parabolas should be observed:
a) vertex
b) axis of symmetry
c) orientation/opening of the graph (upward or
downward)
d) x – intercept/s
e.) y – intercept
f) maximum / minimum point of the graph
g) domain and range of the function
- What is vertex?
- Leoneza, please read the definition of vertex.
Vertex
The vertex (h, k) can be found by (1) using
−𝑏
4𝑎𝑐−𝑏 2
the formula ℎ = 2𝑎 and 𝑘 = 4𝑎 or by
(2) transforming the function to its vertex
form. You can just choose either of the
two, whichever is more convenient to you.
- Thank you, Leoneza. So, vertex in other words is the turning
point which is either the highest or the lowest point of the graph
as you can see in the illustration.






 - Now, let us know what is the axis of symmetry.
 Axis of symmetry
Every parabola has an axis of symmetry which is the vertical line
that divides the graph into two perfect halves. It can be expressed
as an equation in the form x = h, where h can be found in the vertex
(h, k).
- In the illustration, the axis of symmetry is this, the broken lines
that you see.
- Iza, please read what is opening of the graph.
Orientation/opening of the graph
If the value of a is positive or if 𝑎 > 0, the
parabola opens upward. If the value of a is
negative or if 𝑎 < 0, the parabola opens
downward.
- So, you can determine the opening of the graph through the given
value of a.
- Now, x – intercept/s
The x – intercept/s are the points at which the parabola intersects
or touches the x-axis. The value of the x-intercept is actually the
roots/zeros of the quadratic function. Thus, in order for you to
determine the x-intercepts of the graph, you need to solve for the
roots of the function. A parabola may have no, one or two xintercepts.
- We can get the x-intercept by using the 4 methods of solving
quadratic equations such as extracting square roots, factoring,
completing the square, and quadratic formula.
- The y – intercept is the point at which the
parabola passes through the y-axis. To get
the y-intercept, set the value of x into 0.
- Next, y – intercept. Crislyn, kindly read.
- We can determine the y-intercept if we let the x to 0, for example.
- Next, Maximum / minimum point of the graph
When the parabola opens up, the vertex is the lowest point on the
graph — called the minimum, or min. When the parabola opens
down, the vertex is the highest point on the graph — called the
maximum, or max. The maximum or the minimum value of the
graph is the k value of the vertex. Use the formula 𝑘 =
get the value of k.
4𝑎𝑐−𝑏 2
4𝑎
to
- Next, the domain and range of the quadratic function.
- What is the domain of the function?
Domain of the function
The domain of the function is all x - values. There are no
restrictions on the domain of this function. The domain is the set
of all real numbers or in equation, {𝑥⁄𝑥 ∈ ℝ}.
- And, the range of the function are all y- values of the function.
Take note that:
The range is y ≥ k, if the graph opens upward.
The range is y ≤ k, if the graph opens downward.
- Let’s have an example:
𝑦 = 𝑥 2 + 6𝑥 − 7
1. Determine the vertex (h, k)
−𝑏
−(6)
−6
ℎ = 2𝑎 = 2(1) = 2 = −𝟑
𝑘=
4𝑎𝑐−𝑏2
4𝑎
=
4(1)(−7)−(6)2
4(1)
=
−28−36
Hence, the vertex is (-3, -16)
4
=
−64
4
= −𝟏𝟔
2. Make a Table of Values
-5
?
x
y
-4
?
-3
-16
0
?
1
?
3. Solve for y
x = -5
x = -4
𝑦 = 𝑥 2 + 6𝑥 − 7
𝑦 = (−5)2 + 6(−5) − 7
𝑦 = 25 + (−30) − 7
𝑦 = −5 − 7
𝒚 = −𝟏𝟐
𝑦 = 𝑥 2 + 6𝑥 − 7
𝑦 = (−4)2 + 6(−4) − 7
𝑦 = 16 + (−24) − 7
𝑦 = −8 − 7
𝒚 = −𝟏𝟓
x=0
x=1
𝑦 = 𝑥 2 + 6𝑥 − 7
𝑦 = (0)2 + 6(0) − 7
𝑦 = 0+0−7
𝒚 = −𝟕
𝑦 = 𝑥 2 + 6𝑥 − 7
𝑦 = (1)2 + 6(1) − 7
𝑦 = 1+6−7
𝒚=𝟎
Complete Table of Values
x
y
-5
-12
-4
-15
-3
-16
0
-7
4. Opening of the graph
Since the value of a is positive, the opening of the graph is
upward.
5. Axis of symmetry
𝑥=ℎ
𝒙 = −𝟑
6. Domain
{𝑥⁄𝑥 ∈ ℝ} or in sentence, x is all set of real numbers.
7. Range
{𝑦⁄𝑦 ≥ 𝑘}
{𝒚⁄𝒚 ≥ −𝟏𝟔}
8. y-intercept
Let x = 0
𝑦 = 𝑥 2 + 6𝑥 − 7
𝑦 = (0)2 + 6(0) − 7
1
0
𝑦 = 0+0−7
𝒚 = −𝟕
Hence, y-intercept is (0, -7)
9. x-intercept
We can get the x-intercept by using the 4 methods of solving
quadratic equations.
Factoring method:
𝑦 = 𝑥 2 + 6𝑥 − 7
Make this a quadratic equation by replacing the y into 0.
0 = 𝑥 2 + 6𝑥 − 7
Then, factor.
0 = 𝑥 2 + 6𝑥 − 7
(𝑥 + 7) (𝑥 − 1)
𝑥+7=0
; 𝑥−1=0
𝒙 = −𝟕 ;
𝒙=𝟏
Hence, the x-intercept is (-7, 0) (1, 0).
- Plot all the points.
- Let’s have an activity.
- Answer what is asked in the worksheet that I’ll give to you.
Direction: Complete the table for x and y with -3 to 3 as the
domains.
Given: 𝑦 = 𝑥 2 − 2𝑥 − 3
x
-3
-2
-1
0
1
2
3
y
(After 10 minutes)
The students will pass their paper
(worksheet) to the teacher.
b. Reporting
- Iza, how can you write the complete table of values of the given - To make the table of values complete, we
should solve for y of the given quadratic
quadratic function?
function.
- Yes, correct! Now, Leoneza, how to get the values of y?
- We get the values of y by using the
values of x from the table we created and
substitute it to the quadratic function we
use.
- What is the next thing to do if we completed the table of values?
- We sketch the graph on the Cartesian
Yes, Crislyn?
plane.
- That’s right!
c. Drills
Individual Activity:
Direction: In the given quadratic function
𝑦 = 𝑥 2 − 2𝑥 − 3, identify the vertex, axis of symmetry, direction
or opening of the graphs.
Group activity:
Direction: Sketch the graph on the Cartesian Plane.
Given: 𝑦 = 𝑥 2 − 2𝑥 − 3
I. Application
Teacher’s Activity
Student’s Response
- Now, I want you to name at least 3 parabolic structures that you
know and describe the aesthetic value of the structures. Write it in
your paper. I’ll give you 5 minutes to answer.
(The students will follow)
J. Generalization
Teacher’s Activity
Student’s Response
- In graphing quadratic functions, what are the properties of the
parabolas that should be observed?
- In graphing quadratic functions, the
following properties of the parabolas
should be observed:
 vertex
 axis of symmetry
 orientation/opening of the graph
(upward or downward)
 x – intercept/s
 y – intercept
 maximum / minimum point of the
graph
 domain and range of the function
- What is vertex?
- The vertex (h, k) can be found by (1)
−𝑏
4𝑎𝑐−𝑏 2
using the formula ℎ = 2𝑎 and 𝑘 = 4𝑎
or by (2) transforming the function to its
vertex form. You can just choose either of
the two, whichever is more convenient to
you.
- What is axis of symmetry?
- Axis of symmetry
Every parabola has an axis of symmetry
which is the vertical line that divides the
graph into two perfect halves. It can be
expressed as an equation in the form x =
h, where h can be found in the vertex (h,
k).
- In the opening of the graph, If the value of a is positive or if 𝑎 > - Iza: Upward, Ma’am.
0, the parabola opens what?
- Very good. How about if the value of a is negative or if 𝑎 < 0, - Crislyn: Downward, Ma’am.
the parabola opens?
- Yes, that’s correct!
- x and y intercepts should also observe in graphing quadratic
function.
- The domain and range also must be observe in graphing - The domain of the function is all x values. There are no restrictions on the
quadratic function. What is domain? Yes, Leoneza?
domain of this function. The domain is the
set of all real numbers.
- How about the range, Maglente?
- The range of the function are all y- values
of the function.
The range is y ≥ k, if the graph opens
upward.
The range is y ≤ k, if the graph opens
downward.
Summary:
IV. Evaluation
Teacher’s Activity
Student’s Response
- Since, we are done with our discussion, let us have an
assessment. In the worksheet, you are going to draw the graphs of
the quadratic functions:
1. y = -(x - 2)2 + 4
2. y = (x + 3)2 – 4
- The teacher will give 15 minutes to answer.
(The students will follow)
Expected Answers:
1.
2.
V. Assignment
Teacher’s Activity
Student’s Response
- For your assignment, you are going to take pictures of objects or
places showing the graph of quadratic function (parabola). Pass it
on Wednesday for our next meeting.
- See you on Wednesday, good bye class.
- Good bye and thank you, Miss Janin!
- End of class -