GrAssign - Zero Method

~ Show your work and write your answers on the attached answer sheet. (Right) -->

~ You can use Notability to record your work on the above doc.

~ Take a picture of your work and include your name on all pages.

~ Upload everything (your work and Desmos' graphs) to Google Classroom.

~ Save as ZeroMeth_LastName

~ Point value: 25 pts

~ Include the following on the first page:

"I pledge my honor, I will not violate the Nazareth Honor Code during this Graded Assignment."

GrAssign_Zeros_V2.pdf

I. Find the polynomial from its zeros

Find the polynomial of degree 3 whose zeros are 1, -2, and 3.

a. Using the zeros, determine the factors of the function.

b. Determine the behavior of the function around these zeros. (Use the number line model.)

c. Sketch a rough graph of what this function might look like. The max/min points are unimportant; determine where the graph is above or below the x-axis.

d. Multiply the factors to obtain the degree 3 polynomial.

e. Using Desmos, graph the polynomial you found in part (d) to verify your rough sketch.

f. Compare your rough graph to the Desmos graph. How did you do - Close? Wrong? Perfect?

II. Analyze the behavior of a rational function

a. Determine the domain of the function.

b. Determine the zeros.

c. Determine the function's behavior around these

Zeros. (Use the number line model)

d. Does this rational function have vertical asymptote(s)?

e. Sketch a rough graph of what this function might look like.

f. Using Desmos, graph the original function.

g. Compare your rough graph to the Desmos graph.

How did you do - close? Wrong? Perfect?

III. Analyze the behavior of a polynomial inequality.

~ The graph holds the solution to the inequality.

~ Contains the zeros of the function.

~ Is the actual graph of a function.

Observe the lines around the regions. They are significant.

a. Determine the zeros of the inequality.
b. Define the zeros.
c. Using the zeros, determine the factors of the function.
d. Write the equation of the function. (Not the inequality).
e. Determine the behavior of the function around the zeros.
f. Using the above information in part (e) generate a number line.
g. The green area contains the solution set. Identify this solution set.
h. Identify the inequality: >, >=, <, <= Explain your answer.
i. Write the polynomial inequality for this graph.

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