Which could be a graph which represents a quadratic that is a perfect square trinomial?

The top choice.

Step-by-step explanation:

If a quadratic function is a perfect square trinomial, its graph will intersect the x-axis exactly once.

Expanded, this is

There is only one value of x which makes the "two" factors equal to zero, and that is -1, where the graph touches the x-axis.

See the attached graph. is the purple graph.

The green graph is an example of a quadratics which is NOT a perfect square. It's the function .