For the following exercises, use the given information about the polynomial..Degree 4. Roots of multiplicity 2 at x = 1/2 and roots of multiplicity 1 at x = 6 and x = −2. y-intercept at (0,18).

For the following exercises, use the given information about the polynomial graph to write the equation.

Degree 4. Roots of multiplicity 2 at x = 1/2 and roots of multiplicity 1 at x = 6 and x = −2. y-intercept at (0,18).

Solutions

Expert Solution

Consider the information provided in the exercise,

The degree is 4 and zeros are at x = 1/2, x = 6, x = -2.

The first zero occurs at x = 1/2. It has a multiplicity of 2.

The second zero occurs at x = 6. It has a multiplicity of 1.

The third root occurs at x = -2. It has a multiplicity of 1.

Combine all this,

f(x) = a(x – 1/2)2(x – 6)(x + 2)

To determine stretch factor a, put y intercept (0, 18) in the equation.

18 = a(0 – 1/2)2(0 – 6)(0 + 2)

18 = (-12/4)a

a = 18 × 4/-12

a = -6

Hence, the polynomial function is f(x) = -6(x – 1/2)2(x – 6)(x + 2).

Junaid answered 1 year ago

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Solutions

Expert Solution

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