Multiplicity and End Behavior of Polynomials

Which equation MOST LIKELY matches the graph? Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• y = x⁴ - x³ + 3x² + 2

• y = -x⁴ + x³ + 5x + 2

• y = x³ - 2x² + 1x + 3

• y = -x³ - 2x² + 1x + 3

If the graph of a function touches the x-axis, what does that mean about the multiplicity of that zero?

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

Use your notes!

• Even

• Odd

• None

Write the factors of the polynomial from the zeros in the graph. Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• (x - 3) (x + 2) (x + 5)

• (x - 5) (x - 2) (x + 3)

• (x + 3) (x + 2) (x + 5)

• (x - 3) (x - 2) (x - 5)

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

• (-2.55, 0), (2.55, 0)

• (-3, 0), (-2, 0), (2, 0), (3, 0)

• (0, 36)

• (0, -3), (0, -2), (0, 2), (0, 3)

In the above graph, which root has a multiplicity of 2?

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

Use your notes!

• -1

• -3

• -120

• 4

Based on the end behavior which option best describes the leading term?

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

Use your notes!

• negative coefficient, even degree

• negative coefficient, odd degree

• negative degree, odd coefficient

• negative degree, even coefficient

Identify the zeros:

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

Use your notes!

• x=-2, x=-1, x=0

• x=-2, x=0

• x=-1, x=0, x=2

• x=-2, x=0, x=1

Match the equation to the graph. Remember to look at your roots, multiplicity, and end behavior!! Use your notes!

• y=-(x+1)(x-2)(x-4)

• y=(x+1)²(x-3)(x-1)³

• y = 3x³ – 2x + 1

• y=(x+1)³(x-3)(x-1)²

What is the degree?

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

Use your notes!

• Positive

• Negative

• Even

• Odd

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