Polynomial Graphs and Roots

Match the graph to the function

• f(x) = -x⁴-x³+5x²-6

• f(x) = x⁴+3x²-3x+1

• f(x) = -x³+2x²-x-6

• f(x) = x⁴+x³+5x²-6

Is the leading coefficient positive or negative

• positive

• negative

What are the zeros?

• x = - 4

• There are none

• x = - 1.5 & 1.5

• x = - 3.5 and 3.5

The graph of f(x) is shown here. Which statement best describes the function?

• The function has an odd degree and a negative leading coefficient.

• The function has an odd degree and a positive leading coefficient.
  

• The function has an even degree and a negative leading coefficient.
  

• The function has an even degree and a positive leading coefficient.
  

Write the factored form of the graph.

• x(x-2)(x-4)(x-1)

• (x+2)(x-1)(x-4)

• (x+1)(x+2)(x-1)(x-4)

• x(x+2)(x-1)(x-4)

Use the graph to determine the solutions.

• -1 and -3

• 1 and -3

• 1 and 3

• -1 and 3

Find the root(s) of the function.

• x = 3

• x = {-3, -1, 2}

• x = {-3, 2}

• x = -1

What is another word for zeros?

• solutions

• x -intercepts

• roots

• All of the these!

What are the zeros of the function?

• 4,1

• 3,1,-2,-5

• -3, -1, 2, 5

• -2,4

Identify the roots

Remember to look at your roots, multiplicity, and end behavior!!

Use your notes!

• x=2, x=6, x=-4

• (x+2)(x+6)(x-4)

• (x-2)(x-6)(x+4)

• x=-2, x=-6, x=4