Question

Desperate for help

Consider the following function: f(x) = -(x+1)(2x-3)(x-6)

a) At what points does f(x) cross the x-axis?
Give the answers from LEAST to GREATEST. The answers are points, so they should have the form (a,b).

b) What degree is the polynomial?
c) Describe its end behavior: moving to the left, the polynomial .
(This could also be asked, as x-values approach negative infinity, the f(x) values….)
d) Describe its end behavior: moving to the right, the polynomial .
(This could also be asked, as x-values approach positive infinity, the f(x) values….)

Answer 1

You've got a polynomial written as a product of binomials. The points where f(x) = 0 are the zeros, the points where the function crosses or touches the x-axis. You can find all of these points by setting each of those binomials = 0 and solving for x. For example: \[(x+1) = 0\]\[x=-1\]So x = -1 is one of the zeros, and written as a point, it would be (-1,0).

The degree of the polynomial is the highest power of x found in the polynomial if fully expanded, or the number of product binomials. You'll want to expand the polynomial so you can sketch the graph to find the end behavior.