Mathematics is used extensively in civil engineering. Various properties of materials used, how they behave under different conditions, etc. are modeled using mathematical functions to determine how they should be used and what is the appropriate choice.
As a simple example of how a quadratic equation can be used in civil engineering, consider the construction of suspension bridge. The diagram below shows the deck and the cable to which the deck is connected with vertical suspenders.
If you would like to know the points along the deck where the length of the vertical suspenders that join the deck and the suspension cable is 2, the equation that has to be solved to determine the same is:
`0.1*(x-7)^2+2 = 4 `
=> `(x - 7)^2 = 2`
=> `x - 7 = sqrt 2` and `x - 7 = -sqrt 2`
=> `x = 7 + sqrt 2` and `x = 7 - sqrt 2`
Quadratic equations are needed in scenarios where the relation between two variables is not linear. For instance in the example provided earlier the distance between the deck and the the suspension cable is not linear. For two values of x the distance is the same.