Answer
See below.
Work Step by Step
It has no x-intercepts when $f(x)$ has no zeros, thus it is always above or below the x-axis. We can find the zeros with the quadratic formula. The quadratic formula is:
$x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$.
This has no results when the expression under the square root is negative,(because this makes the expression undefined), when $b^2-4ac\lt0\\b^2\lt4ac$
