Question

graph the parabola:
$y = (x - 1)^2 - 5$
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 given equation is in vertex form $y=(x-h)^2+k$, where $(h,k)$ is the vertex. Here $h=1$, $k=-5$, so vertex is $(1, -5)$.

Step2: Find left points (x < 1)

Substitute $x=-1$:

$y=(-1-1)^2-5=(-2)^2-5=4-5=-1$, so point $(-1, -1)$

Substitute $x=0$:

$y=(0-1)^2-5=1-5=-4$, so point $(0, -4)$

Step3: Find right points (x > 1)

Substitute $x=2$:

$y=(2-1)^2-5=1-5=-4$, so point $(2, -4)$

Substitute $x=3$:

$y=(3-1)^2-5=4-5=-1$, so point $(3, -1)$

Answer:

Points to plot:

1. Vertex: $(1, -5)$
2. Left of vertex: $(-1, -1)$, $(0, -4)$
3. Right of vertex: $(2, -4)$, $(3, -1)$

Connect these points to graph the parabola.