In: Advanced Math
For the following exercises, use the given information about the polynomial graph to write the equation.
Degree 5. Roots of multiplicity 2 at x = 3 and x = 1, and a root of multiplicity 1 at x = −3. y-intercept at (0, 9)
Consider the information provided in the exercise,
The degree is 5 and zeros are at x = 3, x = 1, x = -3.
The first zero occurs at x = 3. It has a multiplicity of 2.
The second zero occurs at x = 1. It has a multiplicity of 2.
The third root occurs at x = -3. It has a multiplicity of 1.
Combine all this,
f(x) = a(x – 3)2(x – 1)2(x + 3)
To determine stretch factor a, put y intercept (0, 9) in the equation.
9 = a(0 – 3)2(0 – 1)2(0 + 3)
9 = 27a
a = 9/27
a = 1/3
Hence, the function is f(x) = 1/3(x – 3)2(x – 1)2(x + 3).
Hence, the function is f(x) = 1/3(x – 3)2(x – 1)2(x + 3).