Solve applications of quadratics

There are many applications of quadratics, some of them simple enough to make an appearance in your high school mathematics classroom.

Quadratic functions are used widely in science, business and engineering to model physical phenomena and how quantities change over time. The physical parabolic shape of a quadratic can describe the movement of water in a fountain, the movement of a ball (and in fact any object thrown into the air), or the shape of satellite dishes.  

In avalanche control, triggers are often fired onto a mountain face from an adjacent face to create an avalanche. What height does the trigger reach and where does it land? A quadratic can model this perfectly.

Maximum and minimum values of quadratics are used in the study of moving objects and in acceleration and volume problems. Business models also include quadratic functions and are used to help forecast profit and loss.  

When solving practical problems these steps might be helpful:

• Identify the unknown (what are you solving for?) and use clues given to express other relevant quantities in terms of the unknown. Sometimes you will have to introduce a variable to represent the unknown amount.
• Use the practical context to find relationships between the different amounts involved, and construct equations.
• Solve them, often for when they equal zero, or to find the maximum or minimum. 
• Use your common sense and the context of the problem to interpret the results. For example, when finding length, area or time, can these have negative values?

Let's have a look at the following examples.

Examples

Question 1

Question 2

Question 3