Question 102873
You start with:
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f(x) = x^2
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You can rotate it about the x-axis by changing the sign of the function. Call the new function
g(x). So for the first translation (about the x-axis), we have:
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g(x) = -x^2
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Next you want to shift the graph down by 5 units. Do this by just subtracting 5 from the
function. So now we have two translations and the function is:
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g(x) = -x^2 - 5
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We have one more translation to do. To shift the graph to the left 8 units, replace x
by x + 8. [Yep. The +8 shifts the graph to the left. If you had used -8, the graph would
shift to the right.]  Anyhow, the resulting change to g(x) is:
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g(x) = -(x + 8)^2 - 5
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That's the answer. You might want to try plotting a few points of both functions just to 
satisfy yourself of the shifts. Here's a graph of the two. The red graph is f(x) and the
green graph is g(x).
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{{{graph(600,600,-20,20,-20,20,x^2, -(x + 8)^2 -5)}}}
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Hope this helps you out and that you can understand how the answer comes about.
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