Question

Apply the following transformations to this parabola. Y=2(x+3)^2-1
A) reflection in the x-axis, followed by a translation 5 units down.
I got : y = -2(x+3)^2-6
But the answer is y= -2(x+3)^2-4
Why is it -4

And also. How odd you do reflections in the y axis without drawing the graph and just applying to the equation

Answer 1

sx=reflection about the x-axis
(x,y)->(x,-y)
so
(x, 2(x+3)^2-1 ) -> (x, -(2(x+3)^2-1)) = (x, -2(x+3)^2+1)
Now apply the translation of 5 units down to get the answer.

Answer 2

reflection in the y-axis takes

(x,y) -> (-x,y)
Just fold the paper along the y-axis and see what the points do.