Question

Question was provided via image upload.

Explanation:

Step1: Identify vertex form

Quadratic vertex form: $f(x)=a(x-h)^2+k$
Given: $f(x)=-2(x+4)^2+3=-2(x-(-4))^2+3$

Step2: Find vertex

Vertex is $(h,k)=(-4,3)$

Step3: Find axis of symmetry

Axis of symmetry: $x=h$
$x=-4$

Answer:

Vertex: $(-4, 3)$
Equation of axis of symmetry: $x=-4$

(For graphing: Plot the vertex $(-4,3)$, since $a=-2<0$ the parabola opens downward. Use the axis of symmetry $x=-4$ (dashed line) to mirror points, e.g., when $x=-3$, $f(-3)=-2(1)^2+3=1$ so $(-3,1)$ is a point, and its mirror $(-5,1)$ is also on the parabola; connect points to draw the solid downward-opening parabola.)