Question

graph the parabola.
$y=(x + 2)^2 + 3$
plot five points on the parabola: the vertex, two points to the left of the vertex, and two points to the right of the vertex. then click on the graph - a - function button.

Explanation:

Step1: Find the vertex

The vertex form of a parabola is $y=a(x-h)^2+k$, where $(h,k)$ is the vertex. For $y=(x+2)^2+3$, rewrite as $y=(x-(-2))^2+3$, so vertex is $(-2, 3)$.

Step2: Find left points (x=-3, x=-4)

For $x=-3$: $y=(-3+2)^2+3=(-1)^2+3=1+3=4$, so point $(-3,4)$.
For $x=-4$: $y=(-4+2)^2+3=(-2)^2+3=4+3=7$, so point $(-4,7)$.

Step3: Find right points (x=0, x=1)

For $x=0$: $y=(0+2)^2+3=(2)^2+3=4+3=7$, so point $(0,7)$.
For $x=1$: $y=(1+2)^2+3=(3)^2+3=9+3=12$, so point $(1,12)$.

Answer:

Five points to plot:

1. Vertex: $(-2, 3)$
2. Left of vertex: $(-3, 4)$, $(-4, 7)$
3. Right of vertex: $(0, 7)$, $(1, 12)$