SOLUTION: For x^4-6x^3+9x^2 A) use the coefficient test to determine the graph�s end behavior B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis a

Question 1100633: For x^4-6x^3+9x^2
A) use the coefficient test to determine the graph�s end behavior
B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.
C) Find the y-intercept.
D) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.
E) Find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

For x^4-6x^3+9x^2

A) use the coefficient test to determine the graph�s end behavior

The degree of the polynomial is even, and the leading coefficient is positive, so the function value is going to positive infinity on both ends.

B) Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept.

There are two double roots, at x=0 and x=3. Since they are double roots, the graph just touches the x-axis at those points,

Note the answers to parts A and B tell us that the function value is never negative.

C) Find the y-intercept.

Set x equal to 0; the function value is 0. So the y-intercept is the origin.
(But we already knew that, because 0 is a root.)

D) Determine whether the graph has y-axis symmetry, origin symmetry, or neither.

It is a polynomial function with terms that are both even and odd powers, so it has neither y-axis symmetry nor origin symmetry.

E) Find a few additional points and graph the function. Use the maximum number of turning points to check whether it is drawn correctly.

I'm not sure what the instructions are asking you to do here....

Here is a graph:

RELATED QUESTIONS
For the equation x^4-6x^3+9x^2 A) use the coefficient test to determine the graph�s end... (answered by ikleyn)

Use the following information to graph the polynomial on graph paper f(x) =... (answered by robertb)

Complete the following: (a) Use the Leading Coefficient Test to determine the graph's... (answered by josgarithmetic)

Use the leading coefficient test to determine the end behavior of the polynomial fuction (answered by stanbon)

For the polynomial, state (a)the degree (b)whether it is odd, even or neither (c)end... (answered by htmentor)

Use the Leading Coefficient Test to determine the end behavior of the polynomial... (answered by josgarithmetic)

How do I determine the end behavior of the graph of the function? f(x)=-3x^6+2x^4+4x^3-2 (answered by ewatrrr)

f(x) = 3 - 1/2x^2 a)state the degree and the leading coefficient of f b)state the end (answered by stanbon)

1)Given f(X)= x�-5x: a)Use the leading coefficient test to determine the end result... (answered by stanbon)