Question

Can you help me elaborate on this? I know the right answer is f(x)=(x+1)^2-1. I got the answer by process of elimination. I’m now stuck at is the steps taken to get to the answer.

Answer 1

In the given graph, we can observe a parabola.

According to the graph, its vertex is located at (-1,-1)

The answer options are written in vertex form:

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

Where (h,k) are the coordinates of the vertex. So, h=-1 and k=-1.

If we replace these values into the formula we obtain:

$\begin{gathered} y=(x-(-1))^2+(-1) \\ y=(x+1)^2-1 \end{gathered}$

The answer is:

$f(x)=(x+1)^2-1$