Select the correct answer. Which statement is true about the extreme value of the given quadratic equation? y=-3x^2+12x-33 A. The equation has a minimum value with a y-coordinate of -27 B. The equation has a maximum value with a y-coordinate of -21 C. The equation has a maximum value with a y-coordinate of -27 D. The equation has a minimum value with a y-coordinate of -21 D A B B C

To find the extreme value of the quadratic equation $y=-3x^{2}+12x-33$, we need to find the vertex of the parabola.<br /><br />The vertex form of a quadratic equation is given by $y=a(x-h)^{2}+k$, where $(h,k)$ represents the vertex of the parabola.<br /><br />Comparing the given equation with the vertex form, we can see that the vertex of the parabola is $(h,k)=(2,21)$.<br /><br />Since the coefficient of $x^{2}$ is negative, the parabola opens downwards. Therefore, the vertex represents the maximum value of the equation.<br /><br />Therefore, the correct answer is B. The equation has a maximum value with a y-coordinate of $-21$.