What are the key features of these polynomial functions?

[mathandphysic]

first function: f(x)= x^3-3x^2-6x+8
2nd function: f(x)= x^4-10x^3+35x^2-50x+24

1)whats y intercepts
2)whats x intercepts (zeros)
3)turning points
4)table and graph with appropriate scales
5)intervals of increase/decrease after you determined turning points
6)end behavior
7)symmetry: odd or even

for numbers 1 and 2 i think you have to put the functions onto the graphing calculator and find the y and x intercepts. i did that and i got 8 for the y intercept, -2, 1, 4 for the x intercept of the first function. for the 2nd function i think the y intercept is 30 and the x intercept is 1, 2 , 3, 4. are those intercepts right? that is by far all i know about this whole problem. i know how to graph the functions but how do i make table? I need help on turning points, intervals, end behavior, and symmetry of both functions. thanks for helping.

 

[SammyS]

To find the y-intercept plug-in x = 0. (Your answer is incorrect for the second function.)

Do you know what a turning point is? Your graphing calculator should be able to help you find these.

Do you know what it means for a function to be increasing? ... decreasing?

 

[eumyang]

first function: f(x)= x^3-3x^2-6x+8
2nd function: f(x)= x^4-10x^3+35x^2-50x+24

1)whats y intercepts
2)whats x intercepts (zeros)
3)turning points
4)table and graph with appropriate scales
5)intervals of increase/decrease after you determined turning points
6)end behavior
7)symmetry: odd or even

For #6, look up Leading Term Test for Polynomials.
For #7, are you supposed to find the symmetry by looking at the graph, or algebraically? If algebraically, this involves finding f(-x).

 

[HallsofIvy]

One problem is that you have put these into the 'precaculus' section. While, if you are able to completely factor the polynomials, you can "reason out" the answers, it is far simpler to find first and second derivatives to answer the question. Was this question specifically for a "PreCalculus" class or do have you had "derivatives"?