Question

If an equation has a discriminant of zero, how many times will the graph touch the x–axis?

Answer 1

Once, as there is a double root. Namely:
\[x=\frac{-b}{2a}\]

Answer 2

There are altogether 3 cases.

If disc is GREATER than zero, then TWICE.
If disc is ZERO, then ONCE.
If disc is LESSER than zero, then NEVER.

Answer 3

Thank you!