is a quadratic function. So lets write it down in a standard way . Now you can easily identify

Leading coefficient a is positive so parabola will be facing upwards (don't how to express myself, poor English).

The function/expression is nonnegative for those values of x where parabola is on or above the abscissa, so to have it nonegative for all x would actually mean that the parabola should be completely above the abscissa, or maybe it could touch the abscissa in one point. This actually means that the discriminant should be less than or equal to zero.