The correct answer is D.) f(x)= -2|x-5|+4
In order to find this, we can first look for the vertex. In all absolute value functions, you can find the x value of the vertex by looking at the opposite of the number being add/subtracted inside of the absolute value symbol. In this case, the number is -5 is inside. The opposite would be x = 5.
The y value is always on the outside of the absolute value symbol and you don't have to change the sign. So, the y value should be 4.
Both B and D have these options, but we can differentiate the correct answer from the incorrect one by checking the slope of the line going to the right. Since it is -2, we choose the answer with the -2 in the front. This makes D the correct answer/