Figure A shows a bridge across a river. The arch of the bridge is a parabola, and the six vertical cables that help support the road are equally spaced at $4-m$ intervals. Figure B shows the parabolic arch in an $x-y$ coordinate system, with the left end of the arch at the origin. As is indicated in Figure B, the length of the leftmost cable is $3.072 \ m$. Determine the equation in form $(x-h)^2 = -4p(y-k)$
You know that $h=14$ from the figure and you're only missing p and k. You can easily pull three data points from the figure: (4, 3.072), (28,0), and (0,0). You can use two of those points with ${(x-14)}^2=-4p(y-k)$ to create a two equation, two variable system of equations and solve for p and k. I'll let you solve the rest.