Solve Problems Using Quadratic Equations

So far in this unit, you have learned a variety of methods for solving quadratic equations: graphing, factoring, completing the square, and the quadratic formula. In this final section, you will learn how to apply these skills to solve problems related to situations that can be modelled by quadratic relations, such as paths of projectiles, shapes of parabolic structures, measurement problems involving area, and maximizing revenue.  Learning to use the most appropriate method in a given situation is an important step in becoming a good problem solver.

The first type of problem we’ll solve is a business-related one involving maximizing profits. Regardless of the type of problem you’re solving, always consider the following steps when determining an algebraic solution:

  • Define your variables.
  • Write an equation to model the situation.
  • Simplify the equation, if necessary.
  • Solve the equation using an appropriate method.
  • Consider the allowable values of the unknown. Reject a solution if necessary, providing an
  • appropriate reason.
  • Provide a concluding statement, answering the original question.

Now notice how these steps are applied to the question below:

In the next problem, you’ll learn how to write a quadratic expression to model a rectangular area. This is a common question used by teachers for this grade level!

Another common application problem is one involving an object moving at a parabolic trajectory, such as a rock thrown off a cliff or a ball kicked into the air. In case you come across something like that, here’s how you can solve it:

By now, you should have developed an appreciation towards the versatility of using quadratic equations to solve real-life problems. If you’d like more examples, I have compiled a list of video links below which you can watch to further your understanding.