Determine X Values where the Quadratic Equation y = -x² is Positive

To solve the problem, we need to understand when the function $y = -x^2$ is greater than 0.

1. **Analysis of the Function**: The given function is $y = -x^2$. Here, $y$ represents the output of the quadratic expression, where the coefficient of $x^2$ is negative ($-1$). This means that for every input $x$, the output is the negative of $x^2$.

2. **Properties of the Square**: The expression $x^2$ is always non-negative, i.e., $x^2 \geq 0$ for all real numbers $x$. This implies:

• For $x = 0$, $x^2 = 0$.
• For any non-zero $x$, $x^2 > 0$.

3. **Impact of the Negative Sign**: Since $y = -x^2$:

• If $x^2 = 0$ (which happens when $x = 0$), then $y = 0$.
• If $x^2 > 0$ (which happens when $x \ne 0$), then $y < 0$.

4. **Conclusion on Positivity**: There are no values of $x$ for which $y = -x^2$ is greater than 0, as $y \leq 0$ for all real $x$. Thus, the function is never positive.

Therefore, the solution to this problem is No $x$.