2025 Graphing Polynomials 3-1

Multiple Choice

Do Now

Identify the zeros:

• x=-2, x=-1, x=0
• x=-2, x=0
• x=-1, x=0, x=2
• x=-2, x=0, x=1

Multiple Choice

You have a job that pays you $1500 per month. But 30% is paid in taxes. How much do you actually get paid?

• I don't need money I'll live on the land

• $450

• $1950

• $1050

Multiple Choice

A boy is 2 years old, his brother is half as old as him. When the first boy is 100, how old will his brother be?

• 82

• 75

• 99

• 92

Multiple Choice

As the exponent increases in the function f(x) = x^n, what happens to the graphs in Quadrant I? Which quadrants do the graphs pass through?

• The graphs become steeper

• The graphs flatten out

• The graphs remain unchanged

• The graphs shift to the left

Multiple Choice

What is the standard form of the polynomial represented by the expression -4x + 9 + 2x³?

• 2x³ - 4x + 9

• -4x + 2x³ + 9

• 2x³ + 9 - 4x

• 2x³ - 4x - 9

Reorder

Rewrite $$-4+9x^2-2x+x^3-8x^5$$ in standard form.

• $$-8x^5$$

• $$+x^3$$

• $$+9x^2$$

• $$-2x$$

• $$-4$$

1

2

3

4

5

• 1
• 2
• 3
• 4
• 5

Multiple Choice

How do we know the ocean is friendly?

• It has water

• It has salt

• It waves

Multiple Choice

How do the sign of the leading coefficient and the degree of a polynomial affect the end behavior of the graph of a polynomial function?

• They determine the direction of the graph as x approaches infinity.

• They have no effect on the graph's end behavior.

• They only affect the y-intercept of the graph.

• They determine the number of x-intercepts.

Multiple Choice

Why was the equal sign so humble?

• Because she knew that's better than being proud all the time..

• Because she knew she wasn’t greater than or less than anyone else.

• Because she knew she wasn’t right all the time.

• Because she knew she was impossible to solve.

Multiple Choice

Based on the end behavior of the polynomial, what is the degree of the polynomial?

• a negative real number
• a positive real number
• an odd real number
• an even real number

Multiple Choice

What is the degree?

• Positive
• Negative
• Odd
• Even

Multiple Choice

Choose the answer that best describes the leading coefficient and the degree of the polynomial graph.

• Positive/Even
• Negative/Even
• Positive/Odd
• Negative/Odd

Multiple Choice

Use the leading coefficient and degree of the polynomial function to determine the end behavior of each graph. What is the end behavior of f(x) = 2x^6 - 5x^5 + 6x^4 - x^3 + 4x^2 - x + 1?

• The graph rises to the right and falls to the left.

• The graph falls to the right and rises to the left.

• The graph rises on both ends.

• The graph falls on both ends.

Multiple Choice

What is the answer to this equation?

5 + 5 ÷ 5 + 5 x 5 - 5 = ?

• 5

• 30

• 26

• 22

Multiple Choice

How can you use a table of values to identify key features and sketch a graph of the function?

• By identifying the zeros of the function

• By determining the intervals of increase and decrease

• By finding the maximum and minimum values

• By calculating the derivative of the function

Multiple Choice

What are the coordinates of the relative minimum and relative maximum points for the polynomial function f(x) = -0.5x^4 + 3x^2 + 2?

• (0, 2) and (-2, 6)

• (0, 2) and (2, 6)

• (-2, 6) and (2, 6)

• (0, 2) and (0, 0)

Math Response

How many total turning points (minimums and maximums) does this function have?

Type answer here

Correct Answer: 4

Deg^°

Rad

Multiple Choice

During a snowstorm, John measured the total snowfall accumulated at the end of each hour.  He recorded his results in the table below.  What is the approximate average rate of change of the snowfall between 1 p.m. and 6 p.m.?

• 0.7 inch/hour
• 0.9 inch/hour
• 1.1 inch/hour
• 1.4 inch/hour

Multiple Choice

What is the value of the circle?

• 3

• 7

• 10

• 14

Multiple Choice

Consider the polynomial function f(x) = x^5 + 18x^2 + 10x + 1. What is the average rate of change of the function over the interval [0, 2]?

• 2.5

• 3.0

• 4.0

• 5.0

Multiple Choice

How can you sketch a graph of the polynomial function f from a verbal description?

• Identify the x-intercepts and turning points

• Determine the end behavior

• Estimate the function values

• All of the above

Multiple Choice

There are 12 eggs in a dozen. You bought 3 dozens of eggs. How many eggs do you have?

• 12

• 24

• 36

• Who needs that many eggs?

Open Ended

How long will it take the candle to burn completely?

How do you know?

Multiple Choice

Which of the following intervals has the largest average rate of change?

• [13,14]
• [13, 17]
• [16, 17]
• [16, 19]

Multiple Choice

What seems odd about math?

• Numbers that aren't divisible by two
• Everything 

Multiple Choice

You should never start a conversation with Pi.

• It’ll just end in 3.

• It’ll just go on until you eat a pie.

• It’ll just go on forever.

• It’ll just end if you eat a pie.

Multiple Choice

The polynomial function

$$p\left(m\right)=0.006m^3-1.8m+87.12$$

can be used to determine the price of one share of a mutual fund over the past 18 months, where 𝑚 represents the number of months ago. What does the value of 𝑝(15) represent?

• the price of 15 shares of the mutual fund a year ago

• the price of 1 share of the mutual fund 15 months ago

• the price of 15 shares of the mutual fund 15 months ago

• the price of 1 share of the mutual fund 15 months from now

Multiple Choice

What is the end behavior of polynomial functions based on their degree and leading coefficient?

• It is always increasing

• It is always decreasing

• It depends on the degree and leading coefficient

• It is constant

Open Ended

What is the relationship between the degree and leading coefficient of a polynomial function and the end behavior of the polynomial?

Open Ended

Exit Ticket

Analyze the graph of the given function f as follows: (a) Determine the end behavior: find the power function that the graph of f resembles for large values of |x|. (b) Find the x- and y-intercepts of the graph. (c) Determine whether the graph crosses or touches the x-axis at each x-intercept. (d) Graph f using a graphing utility. (e) Use the graph to determine the local maxima and local minima, if any exist. Round turning points to two decimal places. (f) Use the information obtained in (a) - (e) to draw a complete graph of f by hand. Label all intercepts and turning points. (g) Find the domain of f. Use the graph to find the range of f. (h) Use the graph to determine where f is increasing and where f is decreasing. $$f(x)=x^2(x+2)$$