Which statement is true about the extreme value of the given quadratic equation?
y = -3.2 + 12x – 33
o a. the equation has a maximum value with a y-coordinate of -27.
b.
the equation has a maximum value with a y-coordinate of -21.
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c.
the equation has a minimum value with a y-coordinate of -21.
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d.
the equation has a minimum value with a y-coordinate of -27.
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Option B.  The equation has a maximum value with a y-coordinate of -21.

Step-by-step explanation:

The correct quadratic equation is

This is a vertical parabola open downward (the leading coefficient is negative)

The vertex represent a maximum

Convert to vertex form

Factor -3

Complete the square

Rewrite as perfect squares

The vertex is the point (2,-21)

therefore

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

the quotient is 4x^2 - 27x + 167 with a remainder of -996

step-by-step explanation:

in synthetic division, use -6 as the divisor and use the coefficients {4, -3, 5, 6}:

-6     )   4     -3     5     6

                -24   162 -1002

          4   -27   167   -996

thus, the quotient is 4x^2 - 27x + 167 with a remainder of -996.

note:   your "4x°-3x+5x+6" is ambiguous / incomplete.   i had to assume that you meant '4x^3 - 3x^2 + 5x + 6."

a is the right answer