Part I: Complete the Square
[tex]y=-6x^2 + 36x-12\\ \\ y=-6(x^{2}-6x)-12\\\\ y=-6\left((x-3)^{2}-9 \right)-12\\\\y=-6(x-3)^{2}+54-12\\\\\boxed{y=-6(x-3)^{2}+42}[/tex]
Part II: Graph of the function
See the attached image for the complete graph.
After completing the square, the equation of the quadratic is in vertex form, and so the vertex is at (3, 42).
Also, as the coefficient of [tex]x^2[/tex] is negative, the graph opens down.
Once you figure this out, find the coordinates of some other points on the graph and connect them in the shape of a parabola.
Part III: Line of symmetry
The axis of symmetry is the vertical line passing through the vertex. In this case, it is x = 3.
Part IV: Maximum/minimum value
The maximum/minimum value is the y-coordinate of the vertex. In this case, it is 42.
