Question

Select the correct answer from each drop-down menu. A cable on a suspension bridge can be modeled by this equation, where his the cable's height, in feet, above the roadway d feet away from the entrance to the bridge. h = 0.01d^2 - 0.3d + 22.5 Rewrite the equation in vertex form, and then use it to complete this statement. The (minimum or maximum) height of the cable is (15, 22.5, 20.25, 150) feet from the edge of the bridge and it occurs (150, 22.5, 20.25, 15) feet from the edge of the bridge.

Answer 1

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.