Question

Please show your work.

Answer 1

When you put this into standard form for a parabola, your equation (after much sweating and bleeding from the eyeballs) found by completing the square is: $y- \frac{1520}{200} =- \frac{5}{8} (x+ \frac{12}{5}) ^{2}$, which has a vertex at (-2.4, 7.6).  To find the distance that the directrix is from the vertex (which is also the same distance the focus is from the vertex) we use the fact that $4p=\frac{5}{8}$ (you can omit the negative in front of it cuz distance will always be positive), and $p= \frac{5}{32}$.  Since this is an upside down parabola, the focus is under the vertex ("inside" the parabola) while the directrix is above it.  The directrix is a horizontal line.  Because it is a horizontal line, it is 5/32 above the y-coordinate (or k) or the vertex.  So we add 5/32 to the y-coordinate of the vertex to get 7.6+5/32 and that gives us a directrix of y = 7.76 rounded.