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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