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2.1 What’s Up With the Zeros?

Last updated almost 3 years ago

15 questions

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Let's look at another key feature of polynomials: their zeros. Use desmos.com to graph each of the polynomials below. 

Graph g(x)=(x-2)(x-2)(x+3) on the coordinate plane and identify the following...

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Graph f(x)=(x-2)^{3}(x+4) on the coordinate plane and identify the following...

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Graph f(x)=\frac{1}{2}(x+3)(x+1)(x^{2}+4) on the coordinate plane and identify the following...

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Question 14

14.

Some solutions, or zeros, can’t be seen on a graph. They are imaginary. Explain why the equation x^{2}+4=0 has imaginary solutions. What are they?

Question 15

15.

Can a quadratic equation ever have one real and one imaginary solution? Explain why or why not.

Question 1

1.

Graph

Question 2

2.

X-intercept(s):

Question 3

3.

What is the degree of the polynomial?

Question 4

4.

How are the factors related to the x-intercepts?

Question 5

5.

What is different about the behavior of the graph at x=2 and at x=-3? Why do you think this happens?

Question 6

6.

Graph

Question 7

7.

X-intercept(s):

Question 8

8.

What is the degree of the polynomial?

Question 9

9.

What do you notice about the behavior around the x-intercepts?

Question 10

10.

Graph

Question 11

11.

X-intercept(s):

Question 12

12.

What is the degree of the polynomial?

Question 13

13.

How many solutions are there to the equation f(x)=0?