Solve Quadratic Inequality: When is -(2x-2¼)² Greater Than Zero

Given the function:

$y=-\left(2x-2\frac{1}{4}\right)^2$

Determine for which values of X the following holds:

$f(x) > 0$

To solve this problem, we begin by analyzing the function $y = -\left(2x - 2\frac{1}{4}\right)^2$.

The expression inside the square, $2x - 2\frac{1}{4}$, can take any real value depending on $x$. However, when squared $\left(2x - 2\frac{1}{4}\right)^2$, it becomes non-negative for all real $x$, meaning it is always greater than or equal to zero.

Since $y$ is defined as the negative of this square—$y = -\left(2x - 2\frac{1}{4}\right)^2$—the function $y$ is always less than or equal to zero. In other words, $y \leq 0$ for all real values of $x$.

Therefore, there are no values of $x$ that make $f(x) > 0$, as the function outputs non-positive values exclusively.

Thus, the solution to the problem is No x.