Question

which equation has a graph that is a parabola with a vertex at $(-1, -1)$?
$y = (x + 1)^2 + 1$
$y = (x - 1)^2 - 1$
$y = (x + 1)^2 - 1$

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is $y=(x-h)^2+k$, where $(h,k)$ is the vertex.

Step2: Substitute vertex $(-1,-1)$

Here, $h=-1$, $k=-1$. Substitute into the formula:
$y=(x-(-1))^2+(-1)$

Step3: Simplify the expression

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

Answer:

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