Calculate Negative Area of f(x)=-x²: Quadratic Function Analysis

To solve this problem, follow these steps:

• Step 1: Understand that the function $f(x) = -x^2$ describes a downward-facing parabola with its vertex at the origin (0,0).
• Step 2: Analyze where the function has negative values. For $f(x) = -x^2$, any value of $x \neq 0$ will yield negative output since squaring any nonzero value is positive and multiplying by $-1$ gives a negative result.
• Step 3: Recognize that the point $x = 0$ results in $f(0) = 0$, meaning exactly at the vertex there is no negative value.

From these observations, you can conclude that $f(x)$ is negative for all $x \neq 0$.

Therefore, the solution to the problem is $x \neq 0$ .