Finding Zeros of a Function

Finding Zeros of a Function

Zeros of functions

• Where x=0

• The graph will cross or touch the x-axis

• This graph has zeros of -3, 0, and 2

• So the equation would be $y=x\left(x+3\right)\left(x-2\right)$  

Multiple Choice

What are the zeroes of this graph?

• x = -2, x = 1, x = 4

• x = -4, x = 0, x = 1, x = 2,

• x = -2, x = -1, x = 0, x = 4

• x = -4, x = -1, x = 2

Multiple Choice

Find the root(s) of the function.

• x = 3

• x = {-3, -1, 2}

• x = {-3, 2}

• x = -1

Multiple Choice

What are the zeros of the function?

• 4,1

• 3,1,-2,-5

• -3, -1, 2, 5

• -2,4

Multiple Choice

How many real zeros does the function have?

• None

• 2

• 3

• 4

Multiple Choice

Find the root(s) of the function.

• x = 3

• x = {-3, -1, 2}

• x = {-3, 2}

• x = -1

Multiplicity

• The number of times a solution appears in the factored form of a polynomial

• For example, the equation $y=\left(x-4\right)^2$  has a zero of four with a multiplicity of two

• Notice how it sits on the x-axis

Multiple Choice

What is the equation of this graph in factored form?

• (x - 1)(x + 3)²

• (x - 1)²(x + 3)

• (x + 1)²(x - 3)

• (x + 1)(x - 3)²

Multiple Choice

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)

Even Multiplicities

• Touch the x-axis

Odd Multiplicities

• Intersect the x-axis

Multiple Choice

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

• Even

• Odd

• None

Multiple Choice

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

• Even

• Odd

• None

Multiple Choice

What are the zeros of the polynomial function?

y = (x + 2)(x - 7)³

• -2, 7 multiplicity 3

• -2, 7, 3

• 2, -7 multiplicity 3

• 2, -7, 3

Multiple Choice

Find the correct statement about the zeros.

• −5 is a zero with multiplicity 1

• −5 is a zero with multiplicity 2

• −2 is a zero with multiplicity 1

• 2 is a zero with multiplicity 2

Multiple Choice

What are the zeros of the polynomial function?

y = 3x(x - 6)(x + 5)

• 0, 6, -5

• 6, -5

• 0, -6, 5

• 3, 6, -5

Multiple Choice

What are the

zeros of the polynomial

y = 5(x + 4)(x + 1)(x - 3)?

• -4, -1, 3

• 3, 5, 4, 1

• 4, 1, -3

• 3, -4, -1, 5

Multiple Choice

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)