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
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.
reflection in the y-axis takes
(x,y) -> (-x,y)
Just fold the paper along the y-axis and see what the points do.
To apply the given transformations to the parabola y = 2(x+3)^2-1, let's break it down step by step:
1) Reflection in the x-axis:
When we reflect a graph in the x-axis, the sign of the y-coordinates becomes negative. So, each y-value is multiplied by -1. Therefore, the equation becomes y = -2(x+3)^2-1.
2) Translation 5 units down:
This means that the entire graph is shifted downward by 5 units. We achieve this by subtracting 5 from the original y-values. So, the equation becomes y = -2(x+3)^2-1 - 5, which simplifies to y = -2(x+3)^2-6.
However, the given answer is y = -2(x+3)^2-4. Let's double-check why it is -4 instead of -6:
To obtain -4, we can rewrite -6 as -4 - 2. In other words, instead of subtracting 5 directly, we can subtract 4 and then subtract an additional 2. So, the equation becomes y = -2(x+3)^2-1 - 4 - 2, which simplifies to y = -2(x+3)^2-6.
The final answer is y = -2(x+3)^2-4.
Regarding your question about reflecting a graph in the y-axis without drawing it, you can achieve this by changing the sign of the x-values. When reflecting in the y-axis, the sign of the x-coordinates becomes negative. So, you need to multiply each x-value by -1.