Answer:
D
Step-by-step explanation:
First, note that the graph "bounces" off the x-axis at x=1. This is telling us two things: (1) the graph has a zero at x=1 and (2), since the graph bounces, it has a factor with a multiplicity of 2. Since it is a quadratic, the only way that it can have a multiplicity of two is if the function is a perfect square trinomial. In other words, it can be factored into (x-a)^2.
A, B, and C are not perfect square trinomials. They cannot be factored into the form (x-a)^2.
D is (x-1)(x-1) which equals (x-1)^2, a perfect square trinomial. Its zero is also at x=1. D is correct.
