Introduction to graph of polynomials

1. POLYNOMIALS

2. POLYNOMIAL
FUNCTIONS
MODULE 3

3. OBJECTIVES
At the end of the lesson, the students
should be able to:
1. Recall the concepts of polynomial
expression.
2. Illustrate a polynomial function.
3. Find the degree and the leading term of a
polynomial function.

4. Review: Polynomials
Polynomial Expression
anXn +an-1Xn-1+ an-2Xn-2 + …+ a1X + a0
Polynomial Equation
anXn +an-1Xn-1+ an-2Xn-2 + …+ a1X + a0 = 0
Polynomial expression
Polynomial equation

5. ACTIVITY 1 – Which is which?
Determine whether each of the following is a polynomial expression
or not. On your miniboards write Y is the expression is polynomial; x
if it is not a polynomial. Give reasons.

6. ACTIVITY 1 – Which is which?

7. POLYNOMIAL FUNCTIONS
CONDITIONS:
1. Each exponent is a whole number.
2. Denominators contain no variable in x.
3. No variable is under the radical sign.

8. A polynomial function is a function of the form:
( ) o
n
n
n
n a
x
a
x
a
x
a
x
f +
+
+
+
= −
− 1
1
1 
All of these coefficients are real numbers
n must be a positive integer
The degree of one variable polynomial is the
largest power on any x term in the polynomial.
an ≠ 0

9. POLYNOMIAL FUNCTIONS
( ) o
n
n
n
n a
x
a
x
a
x
a
x
f +
+
+
+
= −
− 1
1
1 
leading term
leading coefficient
constant term

10. 1. f(x) = anXn an-1Xn-1+ an-2Xn-2 + …+ a1X + a0
POLYNOMIAL FUNCTION
• an is called the leading coefficient
• n is the degree of the polynomial
• a0 is called the constant term
*Standard Form – polynomials are written in
descending powers of x.
Polynomial function can be written in
different ways:
2. y = anXn an-1Xn-1+ an-2Xn-2 + …+ a1X + a0
y = x4 + 2x3 –x2 +14x – 56 in factored form is
y = (x2 + 7)(x -2 )(x + 4)

11. Examples:
1.) f(x) = 2x3 – 10x + x4 – 13x2
Standard form:
Degree:
Leading Coefficient:
Constant Term:
2.) y = -45 + 45x2 + 66x + 6x3
Standard form:
Degree:
Leading Coefficient:
Constant Term:
POLYNOMIAL FUNCTION
f(x) = x4 + 2x3 – 13x2 –
10x
4
1
0
f(x)=6x3 + 45x2 + 66x - 45
3
6
-45

12. Polynomial Functions
Polynomial
Function in
General Form
Degree
Name of
Function
1 Linear
2 Quadratic
3 Cubic
4 Quartic
The largest exponent within the polynomial
determines the degree of the polynomial.
e
dx
cx
bx
ax
y +
+
+
+
= 2
3
4
d
cx
bx
ax
y +
+
+
= 2
3
c
bx
ax
y +
+
= 2
b
ax
y +
=

13. ACTIVITY 2 – Fix and Move Them, then Fill
Me Up