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 C

To find the extreme value of the quadratic equation, we need to find the vertex of the parabola.<br /><br />The vertex form of a quadratic equation is given by:<br />$y = a(x-h)^2 + k$<br /><br />where $(h, k)$ represents the vertex of the parabola.<br /><br />Comparing the given equation $y=-3x^{2}+12x-33$ with the vertex form, we can see that:<br />$a = -3$, $h = 2$, and $k = -9$<br /><br />Therefore, the vertex of the parabola is $(2, -9)$.<br /><br />Since the coefficient of $x^2$ is negative, the parabola opens downwards. This means that the vertex represents the maximum value of the equation.<br /><br />So, the correct answer is:<br />C. The equation has a maximum value with a y-coordinate of -9