Write down $F(x)$

The graph $y=F(x)$ is reflected in the $x$-axis and then translated upwards by $3$ units, giving $y=g(x)$ Determine $g(x)$ in completed-square form and state the coordinates of its turning point.

Instead, starting from $y=F(x)$ translate it upwards by $3$ units and then reflect it in the $x$-axis, giving $y=h(x)$ Hence, or otherwise, determine whether $h$ has any $x$-intercepts. Give a reason.