Answer
$b^2-4ac\lt0$
Work Step by Step
Step 1. To find x-intercepts of $f(x)=ax^2+bx+c$, let $f(x)=0$ or $ax^2+bx+c=0$ and solve the equation.
Step 2. We know that when the discriminant $b^2-4ac\lt0$ there will be no real solution, that is no x-intercept.
Step 3. Thus, the graph will have no x-intercepts when $b^2-4ac\lt0$
