Question

graph the parabola.
\\( y=(x-5)^{2}-2 \\)
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. Here $h=5$, $k=-2$, so vertex is $(5, -2)$.

Step2: Find left point 1 (x=3)

Substitute $x=3$ into the equation:
$y=(3-5)^2 - 2 = (-2)^2 - 2 = 4 - 2 = 2$
Point: $(3, 2)$

Step3: Find left point 2 (x=4)

Substitute $x=4$ into the equation:
$y=(4-5)^2 - 2 = (-1)^2 - 2 = 1 - 2 = -1$
Point: $(4, -1)$

Step4: Find right point 1 (x=6)

Substitute $x=6$ into the equation:
$y=(6-5)^2 - 2 = (1)^2 - 2 = 1 - 2 = -1$
Point: $(6, -1)$

Step5: Find right point 2 (x=7)

Substitute $x=7$ into the equation:
$y=(7-5)^2 - 2 = (2)^2 - 2 = 4 - 2 = 2$
Point: $(7, 2)$

Answer:

Five points to plot:

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

Connect these points to graph the parabola.