Answer
Domain: $(-\infty, \infty)$
Range: $(\infty,2]$
Vertex: $(-3,2)$
Axis: $x=-3$
Y-intercept: $(0,-16)$
X-intercepts: $(-4,0)$ and $(-2,0)$
Work Step by Step
Domain: x can have value.
Range: There are no points on the graph that have a y-value greater than 2.
Vertex: Can be seen on the graph.
Axis of parabola: Has the same x-value as the vertex.
Y-intercept: Substitute 0 for x and solve for y.
$$y=-2(0+3)^2+2$$
$$y=-18+2$$
$$y=-16$$
Zeroes: Substitute 0 for y and solve for x.
$$0=-2(x+3)^2+2$$
$$0=-2(x^2+6x+9)+2$$
$$0=-2x^2-12x-16$$
$$2x^2+12x+16=0$$
$$x^2+6x+8=0$$
$$(x+4)(x+2)=0$$
$$x=-4,-2$$
