SOLUTION: I really need help w/ this problem. Anything is appreciated! Let P(x)= -.25x^4 + .875x^3 + x^2 -1.625x -1.5 When factored, P(x)= -.25(x+1)^2 (x-3/2)(x

Algebra ->  Graphs -> SOLUTION: I really need help w/ this problem. Anything is appreciated! Let P(x)= -.25x^4 + .875x^3 + x^2 -1.625x -1.5 When factored, P(x)= -.25(x+1)^2 (x-3/2)(x      Log On


   

Question 1039053: I really need help w/ this problem. Anything is appreciated!
Let P(x)= -.25x^4 + .875x^3 + x^2 -1.625x -1.5

When factored, P(x)= -.25(x+1)^2 (x-3/2)(x-4)
(a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function?

(c) State the y-intercept:

(d) State the real zeros:
(e) Illustrate the graph of P(x).
I really appreciate any help you can offer!
Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


It is a polynomial function. All polynomial functions have a domain of all real numbers.

It is a polynomial function of even degree, namely 4. Therefore both ends take off in the same direction, and that direction is indicated by the sign on the lead coefficient. So both ends of your function decrease without bound if x either increases or decreases without bound.

The y-intercept of any polynomial function is the constant term.

From the factored form, the real zeros are -1 (with a multiplicity of 2), 3/2, and 4, for a total of 4 zeros counting multiplicities which is what we must have for a 4th degree polynomial.



John

My calculator said it, I believe it, that settles it