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1. y = 2. y= MOTIVATION 1.y = 2. y= – 24 GROUP 2 GROUP 1

Teaching Graphs of Polynomial Functions

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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.

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

• Is the polynomial of even degree or odd degree?

Negative Leading Coefficient

Odd Degree

y=

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?

Four(4) turning points

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

y=

y =

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

• Is the polynomial of even degree or odd degree?

Positive Leading Coefficient

Even Degree

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

• 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?

Three(3) turning points

The graph is rising to the left and to the right

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

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

• Is the polynomial of even degree or odd degree?

Negative Leading Coefficient

Even Degree

y = – 24 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?

Three(3) turning points

The graph is falling to the left and to the right

y = – 24 y =

THANK YOU!

FRANZ BROQUEZADEMO TEACHER