Question

I need help with this problem

Answer 1

Part (a)

$g(x)=-3x^2 - 12x-11 \\ \\ =-3(x^2 + 4x)-11 \\ \\ =-3(x^2+4x+4)-11+12 \\ \\ =\boxed{-3(x+2)^2+1}$

So, the vertex is at (-2, 1).

Part (b)

Plot the vertex, (-2,1).

Also, when x = -3, g(x) = -3(-1)² + 1 = -2. Since the graph is symmetric about x = -2, plot (-3, -2) and (-1, -2).

By similar logic, you can also plot (-4, -11) and (0, -11).