Answer
Domain: $(-\infty, \infty)$
Range: $(\infty,1]$
Vertex: $(2,1)$
Axis: $x=-2$
Y-intercept: $(0,-11)$
X-intercepts: $(2+\frac{1}{\sqrt3},0)$ and $(2-\frac{1}{\sqrt3},0)$
Work Step by Step
Domain: x can have value.
Range: There are no points on the graph that have a y-value greater than 1.
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.
$$y=-3(0-2)^2+1$$
$$y=-12+1$$
$$y=-11$$
Zeroes: Substitute 0 for y and solve for x.
$$0=-3(x-2)^2+1$$
$$\frac{1}{3}=(x-2)^2$$
$$x-2=\sqrt{\frac{1}{3}}$$
$$x=2+\sqrt{\frac{1}{3}}, 2-\sqrt{\frac{1}{3}}$$
