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Sagot :
The equation of the parabolic shape of the gate is:
(x - 40)² = -64(y - 25)
What is the equation of a parabola given it’s vertex?
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.
The vertex is at the middle of the parabola, that is, a width of 80/2 = 40 meters and a height of 25 meters, hence h = 40, k = 25, and the equation is:
y = a(x - h)² + k
y = a(x - 40)² + 25
When x = 0, y = 0(start of the arc), hence the leading coefficient is found as follows:
0 = 1600a + 25
a = -25/1600
a = -1/64.
Hence the equation is:
y = -1/64(x - 40)² + 25
(x - 40)² = -64(y - 25)
More can be learned about the equation of a parabola at https://brainly.com/question/17987697
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