U4D8 Polynomial Roots and Graphs Mar20

Last updated 7 months ago
31 questions

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?




What is the degree of the graph?

DEGREE = (# of turns) + 1

Examples:



1 turn, so degree = 2.








3 turns, so degree = 4








2 turns, so degree = 3
1
The graph of y = f(x) is graphed below.
a. Is the graph positive or negative? _______

b. What is the degree of f(x)?
_______

c. What is the constant?
(hint: What is the y-intercept?)
_______
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 from a Graph

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


a. How many roots do you see?

f(x) has _______ roots.

b. What are all the real solutions of f(x) = 0?

The solutions are x = _______ .

c. What is the degree of f(x)?

Degree = _______

Finding the Roots (and more) from a Graph

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


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

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

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

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

1

Example

What is the degree?

1

Example

What is the constant?

1

The graph of f(x) is

Finding the Roots (and more) from a Graph

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

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

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

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

1

Example

What is the degree?

1

Example

What is the constant?

1

The graph of f(x) is

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

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

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)