Question

Select the statements that are true for the graph of y=(x−1)2−6

Answer 1

The graph has a minimum. 
Are there more then one answers?

Answer 2

The two statements that are true is that the graph has a minimum and the vertex is (1, -6).

To find if a graph has a minimum or a maximum, it is very simply. We look for the lead coefficient of x^2 or in vertex form (which it is currently in), the number in front of the parenthesis. In this case, we don't see one, so we assume it is 1. If this number is positive, it means the graph has a minimum. If the graph has a negative, it means there is a maximum.

As for the vertex, we first must know the standard vertex form seen below.

y = a(x - h)^2 + k

In this equation, a is the constant and (h, k) is the vertex. If we look at the equation where it is, we can locate the h and k without doing any mathematical work.

y = (x - 1)^2 - 6

h k

So we know our vertex must be those numbers (1, -6)