Question

The height of a cable that runs between two supports on a suspension bridge can be modeled by a quadratic function () where is the horizontal distance from the first support. The cable is attached to each support at a height of 112 feet. The distance between the supports is 72 feet. The cable is at its lowest height of 10 feet halfway between the two supports.
what is the vertex
axis of symmetry
domain
range
x and y-intercepts

Answer 1

What is the vertex

Its vertex is at (36, -10)

Let us assume that the left edge of the cable is at the origin.

Since the cable is at its lowest height 10 feet halfway between the two supports, the y-coordinate of its lowest point is -10 ft and the x coordinate is 72 ft/2 = 36 ft.

So, its vertex is at (36, -10)

Axis of symmetry

The y-axis.

Since the cable is symmetric about its lowest point, the axis of symmetry is the y-axis.

Domain

The domain is (0, 72).

Since the minimum value of its x-coordinate is at the origin which is x = 0 and the maximum value is at the other support which is at x = 72 ft,

the domain is (0, 72).

Range

The range is (0, -10)

Since the minimum value of the y-coordinate is -10ft and the maximum value is at the origin y = 0,

the range is (0, -10)

x and y-intercepts

The x-intercept is (0, 72) and the y-intercept is (0, 0)

Since the cable is attached at the origin and at 72 feet away  from the origin at the other support, the x-intercept is 0 and 72 ft and the y-intercepts are 0 and 0.

So, the x-intercept is (0, 72) and the y-intercept is (0, 0)

Learn more about quadratic functions here:

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