Characteristics of Polynomial Graphs

Polynomial Graphs Test Review

By Tory Hebert

Topics Covered Last Week

Monday: Parabolas, Vertex, Max/Min, Application Problems

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Tuesday: Cubic Graphs

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Wednesday-Friday: End Behavior of Polynomials ​

Some text here about the topic of discussion

• Finding Max and Min

• -b/2a​

• Finding vertex

• Finding Zeros

• reading graphs for real world applications

• analyzing tables for parabolas ​

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​Some text here about the topic of discussion.

Parabolas ​

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Multiple Choice

Find the equation with the following zeros. (Think FACTORING)

• A

• B

• C

• D

Multiple Choice

Answer the following

• 1

• 2

• 3

• 4

Fill in the Blanks

Multiple Choice

Find the maximum value of the function given.

• 236

• 9

• 54

• 162

Multiple Choice

Which function has no zeros/roots?

• $$y=x^2-5x+6$$  

• $$y=x^2-10x+1$$  

• $$y=x^2-4x+4$$  

• $$y=x^2+8x+16$$  

Multiple Choice

Does the following have any x-intercepts?

• Yes

• No

• Finding domain and range

• increasing and decreasing

• relative max and min values ​

​Some text here about the topic of discussion.

Cubic Function ​

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Fill in the Blanks

Multiple Select

What is true about a cubic function? (select All)

• The domain and range is the same.

• The arrows always point in opposite directions

• There will always be 3 real zeros

• When an<0, the arrows are decreasing

• The degree would be 3

Fill in the Blanks

Multiple Select

On what two intervals is this function negative?

• (-∞,-4)

• (-3,-1.25)

• (-2,∞)

• (-4.75,-3)

• (-1.25,∞)

End Behavior of Polynomials

• remember to use note card

• remember what the largest exponent does to the arrows

• remember how to find zeros

• remember when you may need to use Desmos​

Multiple Choice

Answer the following

• A

• B

• C

• D

Multiple Select

Select all that must be true about the function

• an<0

• an>0

• n is odd

• n is even

• a0 is below the x axis

Multiple Choice

A function has the real zeros 1/2 and -9. The function shows to have arrows point in opposite directions. What is a possible equation for this function.

• $$y=\frac{1}{2}x\left(x+9\right)^2$$  

• $$y=\left(x-\frac{1}{2}\right)\left(x+9\right)$$  

• $$y=\left(2x-1\right)^2\left(x+9\right)$$  

• $$y=\frac{1}{2}x+9x$$  

Multiple Choice

The end behavior of a polynomial function is determined by the degree and the sign of the leading coefficient.
Identify the degree of the polynomial and the sign of the leading coefficient 

• Leading Coefficient Positive
  Degree - Even
• Leading Coefficient Positive
  Degree - Odd
• Leading Coefficient Negative
  Degree - Even
• Leading Coefficient Negative
  Degree - Odd

Multiple Choice

Classify the polynomial by degree.

• quartic
• quintic
• 6th degree polynomial 
• 7th degree polynomial

Multiple Select

Which of the following functions have an even degree? Choose all that apply.

• x⁵+3x²-2

• 4x³-5x⁶+2x+1

Multiple Choice

What could be the equation of the polynomial function shown in this graph?

Multiple Choice

Which of the following equations has the SAME END-BEHAVIOR as this graph?

• y = - x² + 12 - 30

• y = x² + 2x + 7

• y = x³ + 5x² - 2x + 3

• y = - x³ - 4x² + 7x + 9

Multiple Choice

Which of the following equations has the SAME END-BEHAVIOR as this graph?

• y = - 2x⁴ -3x³ + x² -3x + 4

• y = 5x⁴ -3x³ + x² + 2x + 7

• y = 7x³ + 5x² - 2x + 3

• y = - 4x³ - 4x² + 7x + 9

Multiple Choice

(5 seconds...)

What is the end behavior of this polynomial?

g(x) = x⁴ - 3x³ + 5x² + 4x + 8