Question

Use the given information about the polynomial graph to write the equation

degree 4 root of multiplicity 2 at x=4 root of multiplicity 1 at x=-3 and x=-2 y-intercept at (0,-3)

Answer 1

Answer:
`y=-(1)/(32)(x-4)^2 (x+3)(x+2)`

Explanation:

A root of
`x=4` with multiplicity 2 corresponds to a factor of
`(x-4)^2`.

A root of
`x=-3` with multiplicity 1 corresponds to a factor of
`(x+3)`.

A root of
`x=-2` with multiplicity 1 corresponds to a factor of
`(x+2)`.

This means that
`y=a(x-4)^2 (x+3)(x+2)` for some constant a.

Substituting in the coordinates (0, -3),

`-3=a(0-4)^2 (0+3)(0+2) \implies a=-(1)/(32)\\\\\therefore y=-(1)/(32)(x-4)^2 (x+3)(x+2)`