If a quadratic equation only has one real root, describe its relationship with the x-axis.

Answer 1

It touches the x-axis at only one point. If r is the root, it touches the x-axis at (r,f(r)). Depending on whether the sign of the quadratic term is positive or negative, the parabola will open up and be above the x-axis, or it will open down and be below the x-axis, respectively. But in both cases, it touches the x-axis only at (r,f(r)).