0.4x² Inequality Solution: When is the Parabola Above Zero?

To solve this problem, let's break down the given quadratic function:

• Step 1: The function is $y = 0.4x^2$. This is a basic quadratic function where $a = 0.4$, $b = 0$, and $c = 0$.
• Step 2: Since $a = 0.4 > 0$, the parabola opens upwards. The vertex of this parabola is at the point $(0, 0)$.
• Step 3: Address the condition $f(x) > 0$. The function value $y$ is zero exactly at the vertex, $x = 0$. For any other real number value of $x$, the term $x^2$ is positive, and therefore $0.4x^2$ is also positive.

Since $y = 0.4x^2$ will always be greater than zero for every $x \neq 0$, the correct set of values for $x$ where $f(x) > 0$ is all $x$ except $x = 0$. Thus, the solution is expressed as:

$x \ne 0$