The equation of the parabolic arc that accomplishes this task is:
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
The equation of a quadratic function, of vertex (h,k), is given by:
y = a(x - h)² + k
In which a is the leading coefficient.
For this problem, the arc has these following characteristics:
The road under the arc is 20 feet wide with a 6-foot sidewalk on both sides of the road, hence it's total length is of 20 + 2 x 6 = 32 feet, and the peak of the arc will be at h = 16.
Hence:
y = a(x - 16)² + k.
The height is of 0 at x = 0 and x = 32, hence:
0 = 256a + k.
a = -k/256
y = (-k/256)(x - 16)² + k.
In which k is the maximum height of the arc.
More can be learned about the equation of a parabola at https://brainly.com/question/24737967
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