Question

MEDALS!!!!!!!!!!!!!!!

Answer 1

Uhm, do you need help?

Answer 2

When you shift a graph you are adding (or subtracting) some constant number to the function. If you look at a basic graph of a parabola, y=x^2, and compare it to y = x^2 + c, where c is any number, you will see that they look the same, just the second crosses the y axis at the point c instead of the origin. In fact y=x^2 is just the situation where c=0.

Shifting left and right is a bit trickier, you need to add your constant c into the function. For example if you wanted to take the parabola and movie it over to the right, you would write y = (x-c)^2. The reason you subtract to make it move right is because at the value f(c) you want the function to be 0, as this is where the parabola has its x-intercept.

For your question since you want to move the function to the right by 4, you would subtract 4 from x inside the function itself. This gives the answer of g(x) = -abs(x-4).

To gain some intuition on this (for your upcoming tests, of course) I recommend plotting a graph of the functions I just discussed at:

http://www.wolframalpha.com/input/?i=y+%3D+%28x-3%29%5E2