Question

sketch the graph of the quadratic function and the axis of symmetry. state the vertex and give the equation for the axis of symmetry\\
$f(x) = -3(x + 6)^2 + 2$\\
use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.\\
click to enlarge graph

Explanation:

Step1: Identify vertex form

A quadratic in vertex form is $f(x)=a(x-h)^2+k$, where $(h,k)$ is the vertex, and $x=h$ is the axis of symmetry.

Step2: Match given function to form

For $f(x)=-3(x+6)^2+2$, rewrite as $f(x)=-3(x-(-6))^2+2$. Here, $h=-6$, $k=2$.

Step3: Find vertex and symmetry axis

Vertex is $(h,k)=(-6,2)$. Axis of symmetry is $x=h=-6$.

Answer:

Vertex: $(-6, 2)$
Equation of the axis of symmetry: $x=-6$

(For graphing: Plot the vertex $(-6,2)$. Since $a=-3<0$, the parabola opens downward. Use points like $(-5,-1)$ and $(-7,-1)$ (found by substituting $x=-5$ and $x=-7$ into the function) to sketch the solid parabola, and draw a dashed vertical line at $x=-6$ for the axis of symmetry.)