If a<0 and D<0, what can be inferred about f(x)=ax2+bx+c?
f(x) is always negative
When a<0,the graph of f(x)=ax2+bx+c will be in the shape of inverted bowl.
Also, D<0 indicates that f(x) does not cut x-axis
So, the graph of f(x) will look as
From graph, we can see that f(x) is always negative