Solve: When is -(2x-2¼)² Less Than Zero? Complete Solution Guide

The function is given in vertex form: $y = -\left(2x - 2\frac{1}{4}\right)^2$, which translates to $y = -\left(2x - 2.25\right)^2$. The vertex occurs when the expression inside the square is zero, which is at $x = 1\frac{1}{8}$. This is the maximum point due to the negative coefficient, making the function value at the vertex equal to zero.

For $f(x) < 0$, the square term $\left(2x - 2.25\right)^2$ must be non-zero. Thus, set $2x - 2\frac{1}{4} = 0$ to find the $x$ that needs to be excluded:

$2x - 2.25 = 0$

$2x = 2.25$

$x = 1.125$ or $x = 1\frac{1}{8}$

Therefore, for $f(x) < 0$, $x$ should not be equal to $1\frac{1}{8}$.

The correct condition is: $x \neq 1\frac{1}{8}$.