this is a lesson on quadratic functions, it is entailed in this presentation the explanation and differenct examples of a quadratic functions.

1. Lesson 4
QUARTER 2

3. Relation
Relation – pairs of quantities that are related to
each other
Example: The area A of a circle is related to its
radius r by the formula
.
2
r
A 


4. Kenneth
Pearl
Ann
Niña
Mathew
Football
skates
10 speed bike
The arrow diagram illustrates a relation from set A to set B. The
relation is “received”
SET A SET B
“received”

5. Function
When a relation matches each item
from one set with exactly one item
from a different set the relation is
called a function.

6. Definition of a Function
A function is a relationship between two
variables such that each value of the first
variable is paired with exactly one value of the
second variable.
The domain is the set of permitted x values.
The range is the set of found values of y.
These can be called images.

7. Input Output
-3 3
1 1
3
-2
4
{(-3, 3),(1,1),(3,1),(4,-2)}
Input Output
-3 3
1 1
3 -2
4
{(-3, 3),(1,1),(1,-2),(3,3),(4,-2)}
Fig 1
Fig 2
Relations
A Function
Not a Function

8. Is it a Function?
it IS a function.
For each x, there is
only one value of y.
Domain, x Range, y
1 -3.6
2 -3.6
3 4.2
4 4.2
5 10.7
6 12.1
52 52

9. Is it a function?
it is NOT a function
Three different y-values (7,
8, and 10) are paired with
one x-value.
Domain, x Range, y
3 7
3 8
3 10
4 42
10 34
11 18
52 52

10. Two Kinds of Functions
1.Linear Function
2.Quadratic Function

11. Quadratic Function
is a function f defined by an equation
of the form of 𝑦=𝑎𝑥2+ 𝑏𝑥+𝑐 where 𝑎,
𝑏 and 𝑐 are real numbers and 𝑎 ≠ 0.

13. Table of Values
A table of values is a list of numbers that are
used to substitute one variable, such as
within an equation of a line and other
functions, to find the value of the other
variable, or missing number.

14. How to identify linear functions?
- a linear function can be identified by looking at
a table of values, in a linear function the first
differences of y values are equal which
means a constant change in x corresponds to a
constant change in y.

15. In this table, a constant
change of +1 in x
corresponds to constant
change of –3 in y. These
points satisfy a linear
function.
The points from this
table lie on a line.
-3
+1
x y
-2
-1
0
1
2
7
4
1
-2
-5
-3
-3
-3
+1
+1
+1

16. How to identify quadratic functions?
- to determine if the table of values
represents a quadratic function, the second
differences in the y values must be equal

18. How to identify quadratic functions?
Quadratic functions can be represented in an equation
with following forms:
 Standard form
•𝑓(𝑥)=𝑎𝑥2+𝑏𝑥+𝑐, where the value of a, b, c are real
numbers and 𝑎≠0
•𝑓(𝑥)=𝑎𝑥2
•𝑓(𝑥)=𝑎𝑥2+𝑏𝑥
•𝑓(𝑥)=𝑎𝑥2+𝑐

19. How to identify quadratic functions?
Quadratic functions can be represented in an
equation with following forms:
Vertex form
𝑓(𝑥)=𝑎(𝑥−ℎ)2+𝑘, where the vertex is (h, k)
𝑓(𝑥)=𝑎(𝑥−ℎ)2
𝑓(𝑥)=𝑎𝑥2+𝑘

20. How to identify quadratic functions?
Quadratic functions can be represented in an equation
with following forms:
Factored form
o 𝑓(𝑥)=𝑥(𝑎𝑥+𝑏)
o 𝑓(𝑥)=(𝑎𝑥+𝑐)(𝑏𝑥+𝑑)
o 𝑓(𝑥)=(𝑥−ℎ)(𝑥−ℎ)

21. How to identify quadratic functions using equation?
Identify if the given equations is Quadratic Functions or
not.
1. 𝑓(𝑥)=4𝑥−2 – Not QF 6. 𝑓(𝑥)=3𝑥2 – QF in SF
2. 𝑓(𝑥)=𝑥2−9 – QF 7. 𝑓(𝑥)=(𝑥−6)2+7 – QF in VF
3. 𝑓(𝑥)=𝑥2−2𝑥+5 – QF in SF 8. 𝑓(𝑥)= 12(𝑥−13)2 – Not QF
4. 𝑓(𝑥)=𝑥+10 – Not QF 9. 𝑓(𝑥)=−2𝑥+𝑥2+5 – QF in SF
5. 𝑓(𝑥)=(2𝑥−7)(3𝑥+2) – QF in FF 10. 𝑓(𝑥)=𝑥3+3𝑥2 – Not QF