Answer:
Option B. The equation has a maximum value with a y-coordinate of -21.
Step-by-step explanation:
The correct quadratic equation is
[tex]y=-3x^{2}+12x-33[/tex]
This is a vertical parabola open downward (the leading coefficient is negative)
The vertex represent a maximum
Convert to vertex form
Factor -3
[tex]y=-3(x^{2}-4x)-33[/tex]
Complete the square
[tex]y=-3(x^{2}-4x+2^2)-33+12[/tex]
[tex]y=-3(x^{2}-4x+4)-21[/tex]
Rewrite as perfect squares
[tex]y=-3(x-2)^{2}-21[/tex]
The vertex is the point (2,-21)
therefore
The equation has a maximum value with a y-coordinate of -21
