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Math Help - A question about graph reflection.

  1. #1
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    A question about graph reflection.

    This question confused me. I know how to reflect across an axis just fine, but this question asks what an equation would be reflected across a specific line, in this case y = 1. The equation for the original line is f(x) = -(x^2). So, I try reflecting it across the line y = 1 by reflecting is across the x-axis and shifting it up by 1 (g(x)= -f(x) + 1). This gives 17 for g(4). However, the site says the answer is 18. After a little bit of work I find that the only way to get that is g(x) = -f(x) + x/4 + 1. That gives g(0) = 1 and g(4) = 18. Is that correct? And if so, what is a fast way to get to that solution?

    It looks wrong to me....
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  2. #2
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    Re: A question about graph reflection.

    y = -x^2 reflected across the line y = 1 moves the vertex to the point (0,2) ... since the parabola now opens upward,

    y = x^2 + 2

    so ... y(4) = ?
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  3. #3
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    Re: A question about graph reflection.

    Oh, I see. It retains it vertical distance from y = 1? That makes a great deal of sense. Thank you!
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