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