Question

Which statement is true about the extreme value of the given quadratic equation? y=-3x2+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 minimum value with a y-coordinate of -21.D. The equation has a maximum value with a y-coordinate of -27.

Answer 1

Given quadratic equation : $y=-3x^2+12x-33$.

A quadratic equation represents a parabola.

We have leading coefficient is -3, a negative number.

So, it would be a downward parabola and it would have it's vertex point on the top on the parabola.

So, it would obviously have a maximum value.

Let us find the x-coordinate of the parabola first and then y-coordinate of the parabola.

x = -b/2a = -12/2(-3) = -12/-6 = 2.

Plugging x=in given equation, we get

y=-3(2)^2+12(2)-33 = -3(4) +24 -33

  = -12 +24 -33 = -21.

Therefore, maximum value is -21.

Therefore, correct option is :

B. The equation has a maximum value with a y-coordinate of -21.