U4D8 Polynomial Roots and Graphs Mar20

Posljednje ažuriranje about 1 year ago

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Biblioteka

U4D8 Polynomial Roots and Graphs Mar20

Posljednje ažuriranje about 1 year ago

31

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Is the graph positive or negative?

and

What is the DEGREE?

Translation:

From this graph, can you tell if the lead coefficient is positive or negative?

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What is the degree of the graph?

DEGREE = (# of turns) + 1

Examples:

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1 turn, so degree = 2.

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3 turns, so degree = 4

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2 turns, so degree = 3

1

The lead coefficient controls how a graph "ends" (on the right).
A positive lead coefficient causes a graph to increase as the domain increases.
A negative lead coefficient causes a graph to decrease as the domain increases.
All these polynomial graphs have positive lead coefficients except two.
Select the two graphs that have negative lead coefficients.

1

Finding the Roots (and more) from a Graph

The graph of y = f(x) is shown below.

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The graph of y = f(x) is shown below.

null

1

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

1

Example
What is the degree?

1

Example
What is the constant?

1

Finding the Roots (and more) from a Graph

The graph of y = f(x) is shown below.

null

The graph of y = f(x) is shown below.

null

1

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

1

Example
What is the degree?

1

Example
What is the constant?

1

The graph of y = f(x) is shown below.

null

1

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

1

Example
What is the degree?

1

Example
What is the constant?

1

Sketch a graph for a polynomial function with a:
- positive lead coefficient
- degree = 3
- factors: (x + 8),(x + 1), (x - 3)
- y-intercept: (0,-24)

Is the graph positive or negative?

and

What is the DEGREE?

Translation:

From this graph, can you tell if the lead coefficient is positive or negative?

null

What is the degree of the graph?

DEGREE = (# of turns) + 1

Examples:

null

1 turn, so degree = 2.

null

3 turns, so degree = 4

null

2 turns, so degree = 3

1

The lead coefficient controls how a graph "ends" (on the right).
A positive lead coefficient causes a graph to increase as the domain increases.
A negative lead coefficient causes a graph to decrease as the domain increases.
All these polynomial graphs have positive lead coefficients except two.
Select the two graphs that have negative lead coefficients.

Finding the Roots (and more) from a Graph

The graph of y = f(x) is shown below.

null

1

How many x-intercepts does f(x) have?

1

What are all the real solutions of f(x) = 0?
or
What are the roots for f(x)?

1

What is the degree of f(x)?

1

What is the constant for f(x)?

1

The graph of f(x) is

positive

negative

Finding the Roots (and more) from a Graph

The graph of y = f(x) is shown below.

null

1

How many x-intercepts does f(x) have?

1

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

1

This an example of what the degree looks like in a polynomial.
What is the degree of f(x)?

1

This is an example of a constant in a polynomial.
What is the constant for f(x)?

1

The graph of f(x) is

positive

negative

The graph of y = f(x) is shown below.

null

1

How many x-intercepts does f(x) have?

1

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

1

Example
What is the degree?

1

Example
What is the constant?

1

The graph of f(x) is

positive

negative

Sketch a graph for a polynomial function with a:
- positive lead coefficient
- degree = 3
- factors: (x + 8),(x + 1), (x - 3)
- y-intercept: (0,-24)

What are all the real solutions of f(x) = 0?
or
What are the roots for f(x)?

What is the degree of f(x)?

What is the constant for f(x)?

The graph of f(x) is

positive

negative

How many x-intercepts does f(x) have?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

f(x) = (x - 8)(x + 1)(x - 44)(x + 96)

f(x) = (x - 1)(x - 3)(x + 1)(x + 2)

f(x) = (x - 3)(x - 2)(x - 1)(x + 4)

f(x) = (x - 11)(x + 22)(x - 33)(x + 44)

The graph of f(x) is

negative

positive

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

This an example of what the degree looks like in a polynomial.
What is the degree of f(x)?

This is an example of a constant in a polynomial.
What is the constant for f(x)?

The graph of f(x) is

positive

negative

How many x-intercepts does f(x) have?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

f(x) = (x - 2)(x + 1)(x + 3)

f(x) = (x - 2)(x - 1)(x - 3)

f(x) = (x + 2)(x - 1)(x - 3)

f(x) = (x + 2)(x + 1)(x + 3)

The graph of f(x) is

negative

positive

How many x-intercepts does f(x) have?

The graph of f(x) is

positive

negative

U4D8 Polynomial Roots and Graphs Mar20

U4D8 Polynomial Roots and Graphs Mar20

Is the graph positive or negative?

and

What is the DEGREE?

What is the degree of the graph?

Finding the Roots (and more) from a Graph

How many x-intercepts does f(x) have?

The graph of y = f(x) is shown below.

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

ExampleWhat is the degree?

ExampleWhat is the constant?

Finding the Roots (and more) from a Graph

How many x-intercepts does f(x) have?

The graph of y = f(x) is shown below.

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

ExampleWhat is the degree?

ExampleWhat is the constant?

The graph of y = f(x) is shown below.

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

ExampleWhat is the degree?

ExampleWhat is the constant?

Sketch a graph for a polynomial function with a:- positive lead coefficient- degree = 3- factors: (x + 8),(x + 1), (x - 3)- y-intercept: (0,-24)

Is the graph positive or negative?

and

What is the DEGREE?

What is the degree of the graph?

Finding the Roots (and more) from a Graph

How many x-intercepts does f(x) have?

What are all the real solutions of f(x) = 0?orWhat are the roots for f(x)?

What is the degree of f(x)?

What is the constant for f(x)?

The graph of f(x) is

The graph of y = f(x) is shown below.

How many x-intercepts does f(x) have?

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

ExampleWhat is the degree?

ExampleWhat is the constant?

The graph of f(x) is

Finding the Roots (and more) from a Graph

How many x-intercepts does f(x) have?

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

This an example of what the degree looks like in a polynomial.What is the degree of f(x)?

This is an example of a constant in a polynomial.What is the constant for f(x)?

The graph of f(x) is

The graph of y = f(x) is shown below.

How many x-intercepts does f(x) have?

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

ExampleWhat is the degree?

ExampleWhat is the constant?

The graph of f(x) is

The graph of y = f(x) is shown below.

How many x-intercepts does f(x) have?

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

ExampleWhat is the degree?

ExampleWhat is the constant?

The graph of f(x) is

Sketch a graph for a polynomial function with a:- positive lead coefficient- degree = 3- factors: (x + 8),(x + 1), (x - 3)- y-intercept: (0,-24)

What are all the real solutions of f(x) = 0?orWhat are the roots for f(x)?

What is the degree of f(x)?

What is the constant for f(x)?

The graph of f(x) is

How many x-intercepts does f(x) have?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

The graph of f(x) is

What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?

This an example of what the degree looks like in a polynomial.What is the degree of f(x)?

This is an example of a constant in a polynomial.What is the constant for f(x)?

The graph of f(x) is

How many x-intercepts does f(x) have?

Use the x-intercepts and the roots to select the correct factored equation of f(x).

The graph of f(x) is

How many x-intercepts does f(x) have?

The graph of f(x) is

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

Sketch a graph for a polynomial function with a:
- positive lead coefficient
- degree = 3
- factors: (x + 8),(x + 1), (x - 3)
- y-intercept: (0,-24)

What are all the real solutions of f(x) = 0?
or
What are the roots for f(x)?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

This an example of what the degree looks like in a polynomial.
What is the degree of f(x)?

This is an example of a constant in a polynomial.
What is the constant for f(x)?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

Example
What is the degree?

Example
What is the constant?

Sketch a graph for a polynomial function with a:
- positive lead coefficient
- degree = 3
- factors: (x + 8),(x + 1), (x - 3)
- y-intercept: (0,-24)

What are all the real solutions of f(x) = 0?
or
What are the roots for f(x)?

What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?

This an example of what the degree looks like in a polynomial.
What is the degree of f(x)?

This is an example of a constant in a polynomial.
What is the constant for f(x)?