Question

Question was provided via image upload.

Explanation:

Step1: Identify vertex form

The parabola uses vertex form $y=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $y=(x+5)^2+1$, rewrite as $y=(x-(-5))^2+1$. So $h=-5$, $k=1$.
Vertex: $(-5, 1)$

Step2: Find left points (x=-6, -7)

For $x=-6$:
$y=(-6+5)^2+1=(-1)^2+1=1+1=2$
Point: $(-6, 2)$
For $x=-7$:
$y=(-7+5)^2+1=(-2)^2+1=4+1=5$
Point: $(-7, 5)$

Step3: Find right points (x=-4, -3)

For $x=-4$:
$y=(-4+5)^2+1=(1)^2+1=1+1=2$
Point: $(-4, 2)$
For $x=-3$:
$y=(-3+5)^2+1=(2)^2+1=4+1=5$
Point: $(-3, 5)$

Answer:

Five points to plot:

1. Vertex: $(-5, 1)$
2. Left point 1: $(-6, 2)$
3. Left point 2: $(-7, 5)$
4. Right point 1: $(-4, 2)$
5. Right point 2: $(-3, 5)$

(Plot these points on the grid and connect them to form the parabola)