Analyze Domain Behavior: Finding Increasing and Decreasing Intervals of f(x)=5x²-25

To determine the increasing and decreasing domains of the quadratic function $f(x) = 5x^2 - 25$, we begin by analyzing its structure:

This function is a quadratic function of the form $ax^2 + c$. Here, $a = 5$, which is positive. As such, the parabola opens upwards.

The vertex of such a quadratic function, when $b = 0$, is simply at $x = 0$. Thus, the symmetry point of the parabola is based on this vertex.

Since the parabola opens upwards:

• The function is decreasing on the interval $(-\infty, 0)$.
• The function is increasing on the interval $(0, \infty)$.

Therefore, the function $f(x) = 5x^2 - 25$ is:

$x < 0$ decreasing

$0 < x$ increasing

Thus, the correct answer choice for the intervals is the one provided in Choice 4.