Answer
$(x-2)^2=8(y-2)$
Work Step by Step
Step 1. Identify the given quantities: parabola focus $(2,4)$, directrix the x-axis or $y=0$
Step 2. The directrix is horizontal, we can assume the equation as $(x-h)^2=4p(y-k)$
Step 3. The vertex is in the middle between the focus and the directrix $V(2,2)$ which gives $h=2, k=2$
Step 4. The value $p$ is the distance between the vertex and the focus, we have $p=4-2=2$
Step 5. The equation for the parabola can be written as $(x-2)^2=8(y-2)$
