Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x=−2. y-intercept at (0, 4). For the above exercises, use the given information about the polynomial graph to write the equation.

Degree 5. Roots of multiplicity 2 at x = −3 and x = 2 and a root of multiplicity 1 at x=−2. y-intercept at (0, 4).

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

Solutions

Expert Solution

Consider the information provided in the exercise,

The degree is 5 and zeros are at x = -3, x = 2, x - -2.

The first zero occurs at x = -3. It has a multiplicity of 2.

The second zero occurs at x = 2. It has a multiplicity of 2.

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

Combine all this,

f(x) = a(x + 3)2(x – 2)2(x + 2)

To determine stretch factor a, put y intercept (0, 4) in the equation.

4 = a(0 + 3)2(0 – 2)2(0 + 2)

4 = 72a

a = 4/72

a = 1/18

Hence, the function is f(x) = 1/18(x + 3)2(x – 2)2(x + 2).

Junaid answered 1 year ago

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