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 equation of the parabola is in vertex form \( y = a(x - h)^2 + k \), where the vertex is \((h, k)\). For \( y=(x + 2)^2+3 \), we can rewrite \( x + 2 \) as \( x-(-2) \), so \( h=-2 \) and \( k = 3 \). Thus, the vertex is \((-2, 3)\).

Step2: Find points to the left of the vertex

Let's choose \( x=-3 \) (left of \( x = - 2\)): \( y=(-3 + 2)^2+3=(-1)^2+3 = 1 + 3=4 \), so the point is \((-3, 4)\).
Choose \( x=-4 \) (left of \( x=-2\)): \( y=(-4 + 2)^2+3=(-2)^2+3 = 4+3 = 7 \), so the point is \((-4, 7)\).

Step3: Find points to the right of the vertex

Let's choose \( x=-1 \) (right of \( x=-2\)): \( y=(-1 + 2)^2+3=(1)^2+3 = 1+3 = 4 \), so the point is \((-1, 4)\).
Choose \( x = 0\) (right of \( x=-2\)): \( y=(0 + 2)^2+3=(2)^2+3 = 4 + 3=7 \), so the point is \((0, 7)\).

Answer:

The five points are: Vertex \((-2, 3)\), left points \((-3, 4)\), \((-4, 7)\), right points \((-1, 4)\), \((0, 7)\). These points can be plotted on the given coordinate plane to graph the parabola.