SOLUTION: Hello, my wife is in a college algebra class and we are having a problem with one problem. The problem is y=x^4-8x^2-9 and we have to list the intercepts and test for symmetry. W

Question 491587: Hello, my wife is in a college algebra class and we are having a problem with one problem. The problem is y=x^4-8x^2-9 and we have to list the intercepts and test for symmetry. We have been able to factor it down to y=(x^2+1)(x-3)(x+3) and then we are stuck here. The answer in the back of the book shows the intercepts as (3,0) (-3,0) and (0,9) but we are stuck and are unable to come up with any of the answers. the only intercept we could come up with was (0,-9) but that is wrong. Thank you for any and all help you can provide.
Bart
Answer by oberobic(2304) (Show Source): You can put this solution on YOUR website!
Looking at the graph is often helpful:
.

.
This shows the x-intercepts to be: (-3,0) and (3,0).
This shows the y-intercept to be: (0,-9).
.
You also can look this another way using the following substitution:

.
Clearly, two of the roots are

.
But factoring x^2+1 is a problem because to have to solve

In turn, that means:

.
Of course, that defines an imaginary number.

.
Looking back at the original equation:

We can tell by inspection that when x=0, y = -9.
That defines the point (0,-9).
.
So, perhaps the book has an error.
.
Done.

RELATED QUESTIONS
Hi my name is Lissa. This week in my college algebra 2 class we are working on Rational... (answered by stanbon)

Please help me solve this problem (2/3)(x+9)=x+5 This is from a worksheet I have in... (answered by checkley75)

Please help, my daughter is really struggling in Algebra. The problem we are having... (answered by Alan3354)

My son is having a problem with one specific algebra problem. I have not done this in... (answered by Alan3354,ikleyn)

What is 1-3/x divided by x-9/x This problem deals with simplifying complex fractions. I... (answered by solver91311)

Hello, I'm in my last week of my intermediate algebra class and need an additional 14... (answered by Alan3354)

Hi my daughter and I are having a problem solving one of her pre-algebra questions. We... (answered by solver91311)

Hello , my name is Victoria and i need help with my Pre-Algebra homework , & it would be... (answered by rwm)

Hello iam currently taking a college algebra class and my professor gave me this bonus... (answered by richard1234)