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 = x2 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 = x2 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
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.