Zeros & Multiplicity

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

• Even

• Odd

• None

Tags

CCSS.HSF-IF.C.7C

The degree of a polynomial determines...

• the maximum number of x-intercepts

• the number of turning points

• if the end behavior is up or down

• the y-intercept

What are the
zeros of the polynomial
y = 3(x + 4)(x + 1)(x - 3)?

• -4, -1, 3
• 3, -3, 4, 1
• 4, 1, -3
• 3, -4, -1, 3

Tags

CCSS.HSF-IF.C.7C

What are the zeros of the polynomial function?
y = x(x - 6)(x + 5)

• 0, 6, -5
• 6, -5
• 0, -6, 5
• 1, -6, 5

Tags

CCSS.HSF-IF.C.7C

What are the roots of the polynomial function?
y = (x + 2)(x - 7)³

• -2, 7 multiplicity 3
• -2, 7, 3
• 2, -7 multiplicity 3
• 2, -7, 3

Tags

CCSS.HSF-IF.C.7C

Which one of these are not a zero of  $f\left(x\right)=x^2\left(x-1\right)^2\left(x+5\right)$  ?

• 0

• 1

• -5

• -1

Tags

CCSS.HSF-IF.C.7C

What is the multiplicity of the zero x=1 for the function  $f\left(x\right)=x^2\left(x-1\right)^4\left(x+5\right)$  ?

• 2

• 1

• 4

• 3

Tags

CCSS.HSF-IF.C.7C

How does a multiplicity of 2 affect the graph?

• cross

• bounce

• wiggle (change direction)

Tags

CCSS.HSF.BF.B.3

A polynomial function has zeros at -1,2, and 7 (all multiplicity of 1). Write a function rule that could represent this function.

• $f\left(x\right)=\left(x+1\right)\left(x-2\right)\left(x-7\right)$

• $f\left(x\right)=\left(x-1\right)\left(x+2\right)\left(x+7\right)$

• $f\left(x\right)=\left(x+1\right)^2\left(x-2\right)^2\left(x-7\right)^2$

• $f\left(x\right)=\left(x-1\right)^2\left(x+2\right)^2\left(x+7\right)^2$

Tags

CCSS.HSA.APR.B.2

CCSS.HSA.APR.B.3

A polynomial function has zeros at 5 (multiplicity 2), 3 (multiplicity 1), and 0 (multiplicity 4). Write a function rule that could represent this function.

• $f\left(x\right)=x^4\left(x-5\right)^2\left(x-3\right)$

• $f\left(x\right)=x^4\left(x+5\right)^2\left(x+3\right)$

• $f\left(x\right)=x\left(x-5\right)^4\left(x-3\right)^2$

• $f\left(x\right)=x\left(x+5\right)^2\left(x+3\right)^4$

Tags

CCSS.HSA.APR.B.3