Quadratic equations are equations with one variable that have one term with that variable raised to the second power. They can have one or zero terms with that variable not raised to any power. They can have any number of constant terms with no variable at all in them. A large number of jobs involve using the quadratic equation. If you are planning on a career in any of these areas, then you should achieve proficiency in working with them.
Military and Law Enforcement

Quadratic equations are often used to describe the motion of objects that fly through the air. If you plan to join the military and work with artillery or tanks, then you will regularly use the quadratic equation to predict where shells will land. Police also use it in determining the trajectories of bullets and in figuring out the speeds of cars that have been involved in accidents.
Engineering

Engineers of all sorts use these equations. They are necessary for the design of any piece of equipment that is curved, such as auto bodies. Automotive engineers also use them to design brake systems. For similar reasons, aerospace engineers work with them on a regular basis. Electrical and chemical engineers work with many complex systems that involve quadratic equations. So do computer engineers. Audio engineers use these equations to design sound systems that have the best sound quality possible.
Science

Astronomers use quadratic equations to describe the orbits of planets, solar systems and galaxies. Physicists use them to describe different types of motion. Even chemists need them in order to describe certain types of chemical reactions.
Management and Clerical Work

Many management positions also require the use of quadratic equations. Engineering managers and production managers supervise people who use the equations, and so they need to be proficient using them as well. Jobs in human resources involve them too. For example, figuring out how to design and pay for pension plans involves quadratic equations. Insurance agents also need them, as insurance plans are based on models that often involve these types of equations.
Agriculture

Quadratic equations are also used in agriculture. One of these uses is in finding out the optimal arrangement of boundaries to produce the biggest fields and pens given the materials on hand. Area is the length of a surface multiplied by its width. This turns calculations involving areas into quadratic equations.
References
 Photo Credit Jupiterimages/Creatas/Getty Images