The earlier example relates to the use of calculus, not quadratic equations.
The following example is one application of quadratic equations in civil engineering. The cable joining the two towers of the Golden Gate Bridge is modeled by y = 2x^2 - 8x + 12 where y is the height of the cable from the deck and x is the horizontal distance from the left pillar. Where is the height equal to 16 m.
To determine the result solve the equation: 2x^2 - 8x + 12 = 16
=> 2x^2 - 8x - 4 = 0
=> x^2 - 4x - 2 = 0
=> x1 = `(4 + sqrt (16 + 8))/2` and x2 = `(4 - sqrt (16 + 8))/2`
=> x1 = `2 + sqrt 6` and x2 = `2 - sqrt 6`
At the points that are `2 + sqrt 6` and `2 - sqrt 6` m away from the left pillar the height of the hanging cable is 16 m.
Let you want to construct a tank ,with given relation between length and bredth and some relation in width and hight/depth.Condition is that you need max or minimum volume.
V= f(x) .g(x)
when you multi length with width it will quadratic function
so we can say f(x) is quadratic function.Same arguement can be used for g(x)
and g(x)= ax+c (relation between hight and legth or width)
f '(x) will be quadratic wquation in order to define dimensions of the tank for max or min capacity.
It is simple example many more you can get around you.