Engineers and mathematicians apply the simplifying of all manner of equations every day in the course of their work. Scientists in several fields may be required to do the same in the course of a particular project or problem.
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Quadratic equations doesn't help you in life specifically. It just combines a bunch of different math properties. It helps to focus your brain, gain concentration and intellect.
Yes, they commonly appear in free-fall problems.
It really depends what you work in; if you work in science, or in engineering (applied science), you will need the quadratic equation - and a lot more advanced math as well. Examples that involve the quadratic equation are found in abundance in algebra textbooks; for example, an object in free fall.
Why Do We Study Quadratic Equation?In maths class, we are hammered with expressions after expressions of quadratic equations. We are taught how to solve for its roots. We are taught all the necessary methods or mathematical techniques to handle quadratic equations. But after all these, what is the purpose?This is the question many students of maths studies ask.Do we need this "quadratic" knowledge in working life?The communication dish is parabolic in shape. Parabolic is the equivalent to quadratic mathematically. Engineers need to understand quadratic equation to design this beautiful profile.the pan is a wok that is designed using quadratic expression. With this, food can be fried to our liking!Without quadratic equation, who knows how a wok would look like.eye-glass lens are constructed with curves matching that of the quadratic equation.Light is thus controlled to give good image to our eyes.Quadratic equations to the rescue, right?Other examplesare:1) Distance travelled given by the quadratic equation s = ut + (1/2) a t22) Electrical characteristics of a MOSFET (Transistor device)i = k [(Vg - Vt)VD - (1/2)Vd2]So now do you still wonder why you study quadratic equations?with out math these things wouldn't have existed then their would be no dish that will connect us to channels all over the world or like food how can we eat without a pan or even lenses, we all study math for a purpose and it's not just to pass an exam, it's to know more knowledge about whats around us
As you probably suspect, there are no non-mathematical situations in which you would use the quadratic formula.