2.1 What’s Up With the Zeros?

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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...

1

Graph

1

X-intercept(s):

1

What is the degree of the polynomial?

1

How are the factors related to the x-intercepts?

1

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

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

1

Graph

1

X-intercept(s):

1

What is the degree of the polynomial?

1

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

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

1

Graph

1

X-intercept(s):

1

What is the degree of the polynomial?

1

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

1

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?

1

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?

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

2.1 What’s Up With the Zeros?

Graph

X-intercept(s):

What is the degree of the polynomial?

How are the factors related to the x-intercepts?

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

Graph

X-intercept(s):

What is the degree of the polynomial?

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

Graph

X-intercept(s):

What is the degree of the polynomial?

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

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?

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

Graph

X-intercept(s):

What is the degree of the polynomial?

How are the factors related to the x-intercepts?

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

Graph

X-intercept(s):

What is the degree of the polynomial?

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

Graph

X-intercept(s):

What is the degree of the polynomial?

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