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U4D8 Polynomial Roots and Graphs Mar20
By Ali Yasseri
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Last updated about 1 year ago
31 questions
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Question 1
1.
Question 2
2.
Question 3
3.
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.
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The graph of y = f(x) is shown below.
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1
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1
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1
Finding the Roots (and more) from a Graph
The graph of y = f(x) is shown below.
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1
The graph of y = f(x) is shown below.
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The graph of y = f(x) is shown below.
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Question 31
31.
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)
visibility
View drawing
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
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?)
_______
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.
Question 4
4.
Question 5
5.
What are all the real solutions of f(x) = 0?
or
What are the roots for f(x)?
Question 6
6.
What is the degree of f(x)?
Question 7
7.
What is the constant for f(x)?
Question 8
8.
Question 9
9.
Question 10
10.
What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?
Question 11
11.
Question 12
12.
Example
What is the degree?
Question 13
13.
Example
What is the constant?
Question 14
14.
Question 15
15.
Question 16
16.
What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?
Question 17
17.
This an example of what the degree looks like in a polynomial.
What is the degree of f(x)?
Question 18
18.
This is an example of a constant in a polynomial.
What is the constant for f(x)?
Question 19
19.
Question 20
20.
Question 21
21.
What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?
Question 22
22.
Question 23
23.
Example
What is the degree?
Question 24
24.
Example
What is the constant?
Question 25
25.
Question 26
26.
Question 27
27.
What are all the real solutions of f(x) = 0?
or
What are the roots of f(x)?
Question 28
28.
Example
What is the degree?
Question 29
29.
Example
What is the constant?
Question 30
30.
How many x-intercepts does f(x) have?
none
1
2
2, with a bounce
3
The graph of f(x) is
positive
negative
How many x-intercepts does f(x) have?
3
1
2
none
4
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
How many x-intercepts does f(x) have?
3, with a bounce
2
3
none
1
The graph of f(x) is
positive
negative
How many x-intercepts does f(x) have?
none
4
1
3
2
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?
none
2, with 2 bounces
3
4
1
2
The graph of f(x) is
positive
negative