Graphing Polynomials and Multiplicity

Select the polynomial whose zeros and degree are given by: Zeros: – 5(multiplicity of 3), 9(multiplicity of 2), – 2, 4 Degree: 7

• (x + 5)³(x - 9)²(x + 2)(x - 4)

• (x + 5)³(x - 9)²(x + 2)⁷(x - 4)⁷

• (x + 5)³(x - 9)²(x + 2)

• (x + 5)(x - 9)(x + 2)(x - 4)

The degree and the sign of the leading coefficient (positive or negative) of a polynomial determines the behavior of the ends for the graph. Enter the polynomial function into a graphing calculator or online graphing tool to determine the end behavior. f(x) = -2x² + 3x

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to positive infinity. As x goes to positive infinity, y goes to negative infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to positive infinity.

• As x goes to negative infinity, y goes to negative infinity. As x goes to positive infinity, y goes to negative infinity.

List the zeros for this function.

• x= -4, x=3, x= -2

• x= -4, x=3, x=2

• x= -4, x=-3, x=2

• x=4, x= -3, x= -2

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

• y = ^_(x + 2)(x - 1)²

• y = -(x - 2)(x + 1)²

• y = (x - 2)(x + 1)²

• y = -x³

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