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