Teaching Graphs of Polynomial Functions

1. y = 2. y=

MOTIVATION

1.y = 2. y= – 24

GROUP 2

GROUP 1

What to do?Factor the following

expressions!

1. y =

GROUP 1y = (2x+3)()()

2. y= y =

1. y = GROUP 2

y = x(x+3)()()

2. y= – 24 y =

Graphs of Polynomial Functions

(with real roots and no multiplicity)

YOUR ACTIVITY!

Graph of the following functions using Geogebra.

1. y = 2x3 – 7x2 – 7x + 122. y = –x5 + 5x3 – 4x 3. y = x4 – 7x2 + 6x4. y = – x4 + 2x3 + 13x2 – 14x – 24

y =

y=

y =

y= – 24

y = y=

y= – 24y =

y =

• Is the leading coefficient a positive or a negative number?

• Is the polynomial of even degree or odd degree?

y = (2x+3)()()

Positive Leading Coefficient

Odd Degree

y =

• How many turning points do the graph has?

• Observe the end behaviors of the graph on both sides. Is it rising or falling to the left or to the right?

y = (2x+3)()()

Two(2) turning points

The graph is falling to the left and rising to the right.



Negative Leading Coefficient

Odd Degree

y=

y =



Four(4) turning points

The graph is rising to the left and falling to the right

y=

y =



Positive Leading Coefficient

Even Degree

y = y = x(x+3)()()



Three(3) turning points

The graph is rising to the left and to the right

y = y = x(x+3)()()



Negative Leading Coefficient

Even Degree

y = – 24 y =



Three(3) turning points

The graph is falling to the left and to the right

y = – 24 y =

THANK YOU!

FRANZ BROQUEZADEMO TEACHER

Teaching Graphs of Polynomial Functions

Education