Analyzing f(x) < 0 for a Parabola with Non-Intersecting X-Axis

The graph of the function below does not intersect the $x$-axis.

The parabola's vertex is marked A.

Find all values of $x$ where

$f\left(x\right) < 0$.

To solve this problem, we need to determine the range of values where the quadratic function $f(x)$ is negative.

Given that the graph of the function does not intersect the $x$-axis, it suggests that all real-valued outputs of the function have the same sign. This occurs because there are no real roots (solutions) to the equation $f(x) = 0$.

We identify that the quadratic function's parabola is opening upwards (concave up) because it does not intersect the $x$-axis, typically implying the entire parabola is either fully below or fully above the axis, without cutting through it.

If the parabola were above the axis, at the vertex (marked A), the function's value would be positive, and all corresponding function values would also be positive along the width of the parabola. Conversely, if it were below the axis and since the graph maintains this position, the entire function would remain negative.

The problem indicates that the parabola does not intersect or touch the $x$-axis, highlighting that $f(x)$ does not reach zero but maintains positivity or negativity uniformly along the span of $x$.

Since the final answer choice deduces that $f(x)$ does not enter a negative domain by naturally coasting along the positive regional track, the suitable conclusion is that the function has no negative domain, so there are no such values.