1. ## 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....

2. ## Re: A question about graph reflection.

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

$\displaystyle y = x^2 + 2$

so ... $\displaystyle y(4) = ?$

3. ## 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!