Solve the Quadratic Inequality: When is 0.4x² < 0?

To solve this problem, we're given a quadratic function $y = 0.4x^2$. We need to determine for which values of $x$, $f(x) < 0$. Let's start by examining the function.

The given function is quadratic, and it takes the form $y = ax^2$, where $a = 0.4$. It's important to note that the coefficient $a$ is positive.

For quadratic functions in the form $ax^2$, where $a > 0$, the graph of the function is a parabola that opens upwards. This means that the values of the quadratic function are non-negative for all real $x$. Specifically, the value $f(x)$ is always greater than or equal to zero, reaching zero exactly when $x = 0$.

For the inequality $f(x) < 0$ to hold, $y$ would have to be negative. Since the parabola opens upwards and the vertex (the minimum point) is at $y = 0$, there are no real $x$ that satisfy $f(x) < 0$.

Therefore, for the given function $y = 0.4x^2$, there are no values of $x$ for which $f(x) < 0$.

Thus, based on the analysis, the correct choice is that there are no values of $x$ for which $f(x) < 0$ holds, which is No x.