Multiplicity

Which function might have the given graph?

• f(x) = (x - 6)(x + 4)²

• f(x) = (x - 6)²(x + 4)

• f(x) = (x + 6)²(x - 4)

• f(x) = x(x - 6)(x + 4)

State the zeros of the polynomial (include multiplicity):
f(x) = x(x+3)²(x - 2)

• x = 0, 3, 2

• x = 0, -3 (multiplicity of 2), 2

• -3, 2

• 0, 2 (multiplicity of 3)

For each function, determine the real zeros and state the multiplicity of any repeated zeros.

• {0 mult. 3, 5, 2}

• {−2 mult. 3, 3, 1}

• {0 mult. 3, 3, 2}

• {2 mult. 3, 3, 3}

Even Multiplicities have which of the following effects on the x-axis?

• touches and bounces back

• wiggle

• crosses the x-axis

What is the equation in factored form of this graph?

• f(x) = (x-4)(x-1)²(x+2)(x+4)

• f(x) = (x-4)(x+1)²(x+2)(x+4)

• f(x) = (x-4)(x-1)²(x-2)(x+4)

• f(x) = (x+4)(x+1)²(x-2)(x-4)

What could be the function for this graph in factored form?

• f(x) = (x-4)²(x+2)

• f(x) = (x+4)²(x-2)

• f(x) = (x-4)(x+2)²

• f(x) = (x+4)(x-2)²

f(x) = (x+2)(x-3)²(x-4) Which choice best describes the zeros?

• -2, 3 (multiplicity 2), 4

• -2 (multiplicity 2), 3, 4

• 2, -3 (multiplicity 2), -4

• 2 (multiplicity 2), -3, -4

If there is a turning point on the x-axis, what does that mean about the multiplicity of that zero?

• Even

• Odd

• None