Is it possible for a quadratic to have only one root, and not touch the $x$-axis?

Question

Is it possible for a quadratic to have only one root, but its graph crosses the $x$-axis rather than simply touching it?

Answer 1

No. The comments offer many reasons. Here's one from @Joe

If a quadratic has only one root, then it is of the form $=(−)^2$, where $≠0$. If $$ is positive, then the quadratic is always positive or $0$, so it can't cross the $$-axis (if it crossed the $$-axis, then the quadratic would take negative values, which is impossible). Similarly, if $$ is negative, then the quadratic is always negative or $0$, so again it can't cross the $$-axis.