U4D8 Polynomial Roots and Graphs Mar20
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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.
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?
How many x-intercepts does f(x) have?
1
What are all the real solutions of f(x) = 0?orWhat are the roots for f(x)?
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)?
What is the degree of f(x)?
1
What is the constant for f(x)?
What is the constant for f(x)?
1
The graph of f(x) is
The graph of f(x) is
The graph of y = f(x) is shown below.
1
How many x-intercepts does f(x) have?
How many x-intercepts does f(x) have?
1
What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?
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).
Use the x-intercepts and the roots to select the correct factored equation of f(x).
1
Example
What is the degree?
Example
What is the degree?
1
Example
What is the constant?
Example
What is the constant?
1
The graph of f(x) is
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?
How many x-intercepts does f(x) have?
1
What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?
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)?
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)?
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 f(x) is
The graph of y = f(x) is shown below.
1
How many x-intercepts does f(x) have?
How many x-intercepts does f(x) have?
1
What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?
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).
Use the x-intercepts and the roots to select the correct factored equation of f(x).
1
Example
What is the degree?
Example
What is the degree?
1
Example
What is the constant?
Example
What is the constant?
1
The graph of f(x) is
The graph of f(x) is
The graph of y = f(x) is shown below.
1
How many x-intercepts does f(x) have?
How many x-intercepts does f(x) have?
1
What are all the real solutions of f(x) = 0?orWhat are the roots of f(x)?
What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?
1
Example
What is the degree?
Example
What is the degree?
1
Example
What is the constant?
Example
What is the constant?
1
The graph of f(x) is
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)
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)