Answer
a) Below the $x$-axis
b) Above the $x$-axis
Work Step by Step
This question is asking us to design a parabola with two horizontal intercepts, which opens upward. To be sure the parabola has two intercepts when it opens upward we must place its vertex UNDER the $x$-axis. This means $a>0$ and $k<0$.
For example, $a=2$, $k=-1$. The parabola is $$y=(x-h)^2-1,$$ where $h$ can take any real value. let's take $h=3$: $$y=2(x-3)^2-1.$$ Sketch the parabola.
a) The vertex must be below the $x$-axis.
b) If the parabola opens upward, but has no horizontal intercepts, its vertex has to be above the $x$-axis.
