The document discusses graphs of quadratic functions, including key aspects such as the vertex, axis of symmetry, intercepts, and direction of opening. It provides examples of graphing quadratic functions like y = x^2 + 2x - 3 and finding the vertex, axis of symmetry, and intercepts. The document also includes a self-assessment checklist for graphing a quadratic function and determining the vertex, axis of symmetry, opening, intercepts, domain, and range.

1. GRAPHS OF
QUADRATIC
FUNCTION
MATHEMATICS 9
QUARTER 1, WEEK 8

2. MOST ESSENTIAL LEARNING COMPETENCIES
The learner graphs a quadratic function
and determines its
a) vertex,
b) axis of symmetry,
c) domain and range,
d) intercepts and
e) direction of the opening of the graph.
(M9AL-lg-h-i-1)

3. RECALL:

4. Is this a graph of quadratic function?
YES

5. Is this a graph of quadratic function?
NO

6. Is this a graph of quadratic function?
YES

7. Is this a graph of quadratic function?
NO

8. Is this a graph of quadratic function?
NO

9. GRAPHS OF
A QUADRATIC
FUNCTION

10. The graph of a quadratic equation
𝑦 = 𝑎𝑥2
+ 𝑏𝑥 + 𝑐 is a parabola.
When graphing, we want to
include special points/lines in the
graph.
• vertex
• axis of symmetry
• x-intercepts and y-intercept

11. VERTEX
The vertex is
the minimum
or the
maximum
point of the
parabola.

12. AXIS OF SYMMETRY
The axis of symmetry is the
vertical line that passes through
the vertex and divides the
parabola into two equal parts.

13. AXIS OF SYMMETRY
The vertex of the graph
f(x) = −3(x – 2)
2
+ 4 is
(2, 4). The x-coordinate of
the vertex is h = 2.
Therefore, the equation of
the line of the axis of
symmetry is x = 2.

14. OPENING OF
PARABOLA
A parabola may open
upward or downward.
If the value of a is
positive, the parabola
opens upward and if
the value of a is
negative, the
parabola opens
downward.

15. INTERCEPTS
The x-intercepts are
the points where the
parabola crosses the
x-axis.
The y-intercept is the
point where the
parabola crosses the
y-axis

17. 1. Find the axis of symmetry
2. Find the vertex
3. Draw your coordinate and dash in your axis of
symmetry. Plot the point for the vertex.
4. Plot the y – intercept and the point symmetrical
to it. The y-intercept is “c”.
5. Find at least one point on the parabola then draw
the curve.

18. EXAMPLE 1:
Sketch the graph of
𝑦 = 𝑥2
+ 2𝑥 − 3
then determine the special
points and parts.

19. EQUATION INSTRUCTION
𝑦 = 𝑥2
+ 2𝑥 − 3 Group the first two terms and
complete the expression in the
parenthesis to make it a PST by
completing the square.
𝑦 = (𝑥2
+ 2𝑥) − 3
𝑦 = (𝑥2
+ 2𝑥 + 1) − 3 − 1
Add the value of c and subtract the
same value from the constant term
𝑦 = (𝑥 + 1)2
− 4
Factor the resulting PST and write it
as a square of binomial
h = -1 k = - 4 Give the value of ℎ and 𝑘.

22. (-2,-3) (0,-3)
(-3,0) (1,0)

23. LESSON 1: GRAPH OF A QUADRATIC FUNCTION

24. LESSON 1: GRAPH OF A QUADRATIC FUNCTION

27. a. vertex: _______________
b. x-intercepts: _______________
c. y-intercept: _______________
d. axis of symmetry: ___________
e. opening of the graph: _____________
f. domain: ______________
g. range: ______________

28. Advanced Proficient Basic Minimal
Accuracy All the answers are
correct
Most of the answers
are correct.
Some of the answers
are correct.
Little or none of the
answers are correct.
Completion All the assigned work
is complete.
Most the assigned
work is complete.
Some the assigned
work is complete.
Little work is
complete.
Labeling All pars of the graph
are labeled neatly,
clearly
Two sides of the
graph are labeled.
One side of the graph
is labeled.
The graph is not
labeled.
Group Participation All group members
participated in the
activity.
Most group members
participated in the
activity.
Some group members
participated in the
activity.
Few members
participated in the
activity.
Neatness The work is neatly
done.
Neat and somehow
readable.
There were many
erasures on the work
Appears
Exceptionally messy

30. Graph the following quadratic function and determine the vertex, axis of
symmetry, opening of the graph, x-intercepts, y-intercept, domain, and
range.