Question

The main cable of a suspension bridge forms a parabola, described by the equation y = a(x − h)^2 + k.y =height in feet of the cable above the roadwayx =horizontal distance in feet from the left bridge supporta =a constant(h, k) =vertex of the parbolaWhat is the vertex of the parbola?( , ),( , )

Answer 1

Looking at the table, we can see that at y = 7, the other y-values are equidistant from 7.

For example, the two points (52.5, 12) and (157.6, 12) are both 5 horizontal units away from (105, 7). In addition, the points (0, 27) and (210, 27) are both 20 horizontal units from (105, 7)

Hence, the vertex of the parabola is found at this point (105, 7).