You can
put this solution on YOUR website!Rotating the graph y=x^2 about the x-axis does not change it. Dropping the graph down 5 units is like subtracting the value of 5 from the x^2, and shifting the graph left 8 units is like adding 8 to the x. The equation is
, and the graph should look like this:
R^2 Retired = R^3 from SCC
You can
put this solution on YOUR website!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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Hope this helps you out and that you can understand how the answer comes about.
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