Example: In –x^2– 4x+ 5 I would say ok so it has a reflection of the y axis, It moves right 4 units and moves up 5. But the answer is that instead of moving 4 units right, its 4 units LEFT. Why???

Take y = x

^{2}and y= (x-4)^{2 }.The parabolic form is y = a(x MINUS h) PLUS k, where (h, k) is the vertex of the parabola opening up or down depending on the sign of a.

So the vertex is at (0,0) for y = x

^{2}since y = 1(x-0)^{2}+ 0.Now, for y = (x-4)2, note that the vertex (which is essentially the "handle" for the parabola) is now at

(+4, 0).

So despite the (x MINUS 4) being squared, the x coordinate of the vertex was shifted from 0 to 4, which is a shift to the

**right**of 4.Now consider y=(x+4)

^{2}.That's really y = (x - (-4))

^{2}+ 0. So the vertex was moved 4 units to the left from (0, 0) to (-4, 0).Hope this helps.