Question

graph the parabola.
\\( y=(x-2)^{2}+1 \\)
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: Identify the vertex

The parabola is in vertex form $y=(x-h)^2+k$, where $(h,k)$ is the vertex. For $y=(x-2)^2+1$, $h=2$, $k=1$.
Vertex: $(2,1)$

Step2: Find left points (x=0,1)

For $x=0$:

$y=(0-2)^2+1=4+1=5$
Point: $(0,5)$

For $x=1$:

$y=(1-2)^2+1=1+1=2$
Point: $(1,2)$

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

For $x=3$:

$y=(3-2)^2+1=1+1=2$
Point: $(3,2)$

For $x=4$:

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

Answer:

Five points to plot:

1. Vertex: $(2, 1)$
2. Left point 1: $(0, 5)$
3. Left point 2: $(1, 2)$
4. Right point 1: $(3, 2)$
5. Right point 2: $(4, 5)$

Connect these points to graph the parabola.