1) Draw a set of coordinate axes, x and y.
2) Put a downward-pointing parabola on the plane defined in 1)
2a) Put the vertex at (0,20)
2b) Label the x-intercepts (40,0) and (-40,0)
2c) Note how the y-axes cuts the parabola in half. The y-axis is the line of symmetry.
3) We need an equation. What do you know about a downward-pointing parabolas with vertex at (0,20)? This should look familiar . In this case, we know h = 0 and k = 20, so .
4) Solve for the remaining parameter by simple substitution. We have the point (40,0), then . I am SO HAPPY this is a negative value. This results in
5) We're ready. What does the problem statement want? 20m from either end of the base. It's symmetric about the y-axis, so it doesn't matter which side we choose. Let's keep it positive. 20m from (40,0) is (20,0), so we need to find the y-coordinate associated with x = 20. Simple substitution and a little algebra and you are done.
Show what you get for that one.
Let's see you tackle the other problem. It's only a test to see if you can find the focus. Use that general equation from part 3.