Final answer:
The equation can be rewritten in vertex form as h = 0.01(d - 15)^2 - 28.75. The minimum height of the cable is -28.75 feet from the edge of the bridge.
Step-by-step explanation:
The given equation is in the general form ax^2 + bx + c = 0. To rewrite it in vertex form, we need to complete the square. Let's start by factoring out the coefficient of the quadratic term:
h = 0.01(d^2 - 30d + 2250)
Next, we will add and subtract the square of half the coefficient of the linear term inside the parentheses to complete the square:
h = 0.01(d^2 - 30d + 2250 + (225)^2 - (225)^2)
Simplifying, we get:
h = 0.01[(d - 15)^2 + 2250 - 50625]
Further simplification yields:
h = 0.01(d - 15)^2 - 28.75
Now we can determine the vertex of the parabola, which represents the minimum or maximum height of the cable. In vertex form, the vertex is given by (h, k), where h is the x-coordinate and k is the y-coordinate. In this equation, the vertex is (15, -28.75), which means the minimum height of the cable is -28.75 feet from the edge of the bridge.