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

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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) About Me  (Show Source):
You can put this solution on YOUR website!
Looking at the graph is often helpful:
.
graph%28500%2C500%2C-10%2C10%2C-30%2C30%2Cx%5E4-8%2Ax%5E2-9%29
.
This shows the x-intercepts to be: (-3,0) and (3,0).
This shows the y-intercept to be: (0,-9).
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You also can look this another way using the following substitution:
u+=+x%5E2
.
y+=+u%5E2+-8u+-+9
y+=+%28u+%2B1%29%28u-9%29
.
y+=+%28x%5E2%2B1%29%2A%28x%5E2-9%29
y+=+%28x%5E2%2B1%29+%2A+%28x-3%29%28x%2B3%29
.
Clearly, two of the roots are
x+=+3
x+=+-3
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But factoring x^2+1 is a problem because to have to solve
x%5E2+%2B+1+=+0
In turn, that means:
x%5E2+=+-1
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Of course, that defines an imaginary number.
i%5E2+=+-1
.
Looking back at the original equation:
y+=+x%5E4+-8x%5E2+-9
We can tell by inspection that when x=0, y = -9.
That defines the point (0,-9).
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So, perhaps the book has an error.
.
Done.