3. What is the maximum value of $$ f(x)=-4 x^{2}+16 x+12 $$

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Let $$ f(x) = -4x^2 + 16x + 12 $$.

1. Since the coefficient of $$ x^2 $$ is negative, the parabola opens downward, which means the vertex represents the maximum point.

2. The $$ x $$-coordinate of the vertex is given by
   $$
   x = -\frac{b}{2a}
   $$
   where $$ a = -4 $$ and $$ b = 16 $$. Thus,
   $$
   x = -\frac{16}{2(-4)} = -\frac{16}{-8} = 2.
   $$

3. Substitute $$ x = 2 $$ into $$ f(x) $$ to find the maximum value:
   $$
   f(2) = -4(2^2) + 16(2) + 12 = -4(4) + 32 + 12 = -16 + 32 + 12.
   $$
   
4. Simplify the expression:
   $$
   f(2) = 28.
   $$

The maximum value of $$ f(x) $$ is $$ \boxed{28} $$.
The maximum value of $$ f(x) = -4x^2 + 16x + 12 $$ is 28.

What is the maximum value of

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