which equation has a graph that is a parabola with a vertex at (-1, -1)?\no y=(x - 1)^2+1\no y=(x…

Explanation:

Step1: Recall vertex - form of parabola

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

Step2: Identify values of h and k

Given the vertex $(-1,-1)$, so $h=-1$ and $k = - 1$.

Step3: Substitute h and k into vertex - form

Substituting into $y=a(x - h)^2+k$, we get $y=a(x-(-1))^2+(-1)=a(x + 1)^2-1$. When $a = 1$, the equation is $y=(x + 1)^2-1$.

Answer:

$y=(x + 1)^2-1$ (corresponding to the fourth option)