This is a Lesson plan or Lesson Exemplar on Solving situational problems involving parabola in PreCalculus subject.

1. I. Learning Outcomes: At the end of the lesson, students shall be able to:
a. solve situational problems involving parabola;
b. give the importance of the contribution of the concept of parabola in the real world;
c. find and solve situational problems involving parabola.
II. Subject Matter: Situational Problems involving Parabolas
Learning Resources: Analytic and Solid Geometry and Pre-Calculus Teaching Guide (to be written in
APA style)
Skills: drawing, sketching, analysing and solving
Values: Cooperation in the Group
III. Materials: Pictures, marker and illustration board.
IV. Procedure: Inquiry-Based Learning
Teacher’s Activity Students’ Expected Response
A. Daily Routine
B. Motivation: “Act me-You’ll know me”
Mechanics:
1. The students will be grouped into five.
2. Each group will be given different pictures of
certain parabolic objects.
3. A group will choose two representatives: the
guesser and the interpreter
4. The interpreter will act out the given object
while the guesser will name what object that the
interpreter is portraying through asking questions
from the group.
5. The rest of the group will tell the guesser with
“Oo, Hindi, and Pwedi”.
6. The group which can name the object in a
shortest time will be declared as a winner.
Group 1
Group 2.
Group 3
Students have pre-assigned parts in what to do.
Students have pre-assigned parts in what to do
a. bowl
b. tunnel
c. funnel

2. Group 4
Group 5
Among the following objects in the pictures,
what do you think is the common
characteristics?
Do the pictures portray the idea of conic
sections?
What conic section is being portrayed?
Why did you say so?
What do those objects represent?
B. Presentation
The teacher will present the topic and will let the
students read it.
Learning Outcomes:
a. solve situational problems involving
parabola;
b. give the importance of the contribution of
the concept of parabola in the real world;
c. create situational problems involving
parabola.
Okay, let us have an example of a problem
portraying a real life application of parabola. The
students will still stay on their group.
d. hook
e. roller coaster
The objects have all curves lines.
Yes sir!
It is parabola.
Since all objects are parabolic. They all portray a
figure of parabola.
Those objects are the real life application of the
concept of parabola.
” Situational problems involving parabolas”

3. Example:
A satellite dish on the top of the building has a
shape called a paraboloid, where each cross-
section is a parabola. Since radio signals
(parallel to the axis) will bounce off the surface
of the dish to the focus, the receiver should be
placed at the focus. Howfar should the receiver
be from the vertex, if the dish is 12 ft. across,
and 4.5 ft. deep at the vertex?
As you noticed in the problem, do you think that
paraboloid and parabola are the same?
Okay, as it is being stated in the problem,
paraboloid is the shape of the satellite dish, so it is
a solid while its cross section is a parabola.
Therefore, parabola is a part of paraboloid.
Now, what do you think is the position of the
parabola? Is it opening to the left? Right? Up? Or
down?
Since it is opening upward, what is the axis of
asymmetry?
Very good!
Since the parabola is opening upward and the axis
of symmetry is the y-axis, what is then its formula?
So, what will we do with its vertex?
What are the information given in the
problem?
What is being asked in the problem?
How will you simplify of what is being asked?
Given the information in the problem, how can
you illustrate it?
Based on the formula 2
4x ay , how will you
find the distance from the focus to the vertex?
Why can you say that finding the value of a
will solve the given problem?
Yes sir because they are both curves.
No, sir because paraboloid is a solid while parabola
is a plane.
Since it is a satellite dish on the top of the building,
it is opening upward.
The axis of symmetry is the y-axis
The formula is
2
4x ay
The vertex is placed at the origin since its
coordinates is not given, then it is assumed as (0,0).
*The opening of the satellite dish is 12 ft. across.
*The satellite is 4.5 ft. deep from its opening to its
vertex.
The distance that the signal will travel from the
focus to the vertex.
It is simply the distance from the focus to the
vertex.
Every group will have its own illustration.
Based on the formula, to find the distance from the
focus to the vertex, we will just find the value of a.
In the parabola, the variable a means the distance
from the vertex to the focus based on its properties.

4. Given the formula, how will you find the value
of a.
How will you find the value of x and y?
Given the correct illustration of the problem.
How will you find x?
How about for y?
How did you come up of the idea?
What can you conclude then?
To solve for a, how can we use the coordinates
of x and y which is (6, 4.5)?
C. Practice
The class will be grouped again to 5 groups
and will be given different problems which
will be solved within a given allocated time.
They will present their solutions in front of the
class.
1. A satellite dish shaped like a paraboloid,
has diameter 2 .4 ft and depth 0.9 ft. If the
receiver is placed at the focus, how far should
the receiver be from the vertex?
To find the value of a in the formula, we need to
find first the values of x and y in the formula.
We can find the value of x and y by utilizing the
given information in the problem.
To find x, we will utilize the length of the opening
of satellite dish which 12 ft. so , side by side, it has
6 ft. from the axis of symmetry to both endpoint of
the opening.
To find the value of y, we will utilize the given
information which is the 4.5 ft. deep of the satellite
to the vertex.
It is through rectangular coordinate system.
It is therefore being set that x and y is a single point
on the parabola which has now a coordinate (6,
4.5).
We will simply substitute it to the formula.
To substitute, we have:
2
4x ay
where x =6 and y = 4.5
2
6 4 (4.5)
36 (4)(4.5)
36 18
36 18
18 18
2
a
a
a
a
a





Therefore, the distance that the signal has to travel
from the focus to the vertex is 2 ft.
(Solutions will be indicated)
Answer: 0.4 ft

5. 2. If the diameter of the satellite dish from the
previous problem is doubled, with the depth
kept the same, how far should the receiver be
from the vertex?
3. A satellite dish is shaped like a paraboloid,
with the receiver placed at the focus. It is to
have a depth of 0.44 m at the vertex, with the
receiver placed 0.11 m away from the vertex.
What should the diameter of the satellite dish
be?
4. A flashlight is shaped like a paraboloid, so
that if its light bulb is placed at the focus, the
light rays from the bulb will then bounce o↵
the surface in a focused direction that is
parallel to the axis. If the paraboloid has a
depth of 1.8 in and the diameter on its surface
is 6 in, how far should the light source be
placed from the vertex?
5. The towers supporting the cable of a
suspension bridge are 1200 m apart and 170 m
above the bridge it supports. Suppose the cable
hangs, following the shape of a parabola, with
its lowest point 20 m above the bridge. How
high is the cable 120 m away from a tower?
D. Enrichment
The same group of students will be tasked to
go outside and find a situational problem in the
surroundings within in a given allocated time.
After that, students will come back inside the
classroom and will present their situational
problem.
Criteria for the presentation (To be revised
in a form of Analytic Rubrics)
Authenticity – 25 points
Correctness – 30 points
Delivery – 30 points
Teamwork – 15 points
Total – 100 points
E. Values Integration
What values have you developed a while ago
while working with your group?
I will give a checklist and put a check the box
which corresponds to your response on the
following statements in the checklist about
value of cooperation
Answer: 1.6 ft.
Answer: 0.88 m
Answer: 1.25 in
Answer: 116 m
It is the value of teamwork or cooperation with
the group. When all members in the group will
work together, they can easily accomplish the
given task.
(Checklist will be distributed to the students and
they will answer it).

6. Now class, as to giving importance to the
contribution of the concept of parabola, what
do you think is its importance?
E. Evaluation
Directions: Solve for the following situation
problems involving parabolas.
1. An arch in a memorial park, having a
parabolic shape, has a height of 25 feet and a
base width of 30 feet. Find an equation which
models this shape, using the x-axis to represent
the ground. State the focus and directrix.
2. A radio telescope has a parabolic dish with a
diameter of 100 meters. The collected radio
signals are reflected to one collection point,
called the "focal" point, being the focus of the
parabola. If the focal length is 45 meters, find
the depth of the dish, rounded to one decimal
place.
V. Advanced Task
Directions: Read and advance the study about
ellipse, its standard and general equation, and
its center at (h,k) and (0,0).
The contribution of the concept of parabola in the
world is very important since it plays a significant
role especially in constructing establishments and
manufacturing tools and equipment which follow
the concept of parabola.
focus: (0, 91/4), directrix: y = 109/4
y = 250/18
...or about 13.9 meters.