The Quadratic Function

Not only is the quadratic extremely helpful and used in abundance in math class, but it is pertinent in daily life as well- especially in sports. Any ball thrown up into the air will follow the trajectory of a parabola, which of course is the parent function of x squared. In order to find the height, time, or speed of a throw, you must use the quadratic function. This can be used in any sport such as tennis, soccer, football, etc, and a lot in architecture.  In addition to these uses, the quadratic function can be applied when calculating the area of an object or finding the profits a company makes, like in this example:

• Unit Sales = 70,000 - 200P
• Sales in Dollars = Units × Price = (70,000 - 200P) × P = 70,000P - 200P²
• Costs = 700,000 + 110 x (70,000 - 200P) = 700,000 + 7,700,000 - 22,000P = 8,400,000 - 22,000P
• Profit = Sales-Costs = 70,000P - 200P² - (8,400,000 - 22,000P) = -200P² + 92,000P - 8,400,000

 We say all the time in class, "when am I ever going to use this?!" but in reality, you most likely will use it during sometime in your career. There are so many forms of a quadratic, (such as vertex form), but one thing that's always true is the parabolic shape that it graphs. Knowing how to graph is extremely important because it brings an equation to life and it becomes visually apparent how it would look if it were a ball thrown in the air.

Mapping the trajectory of a ball.

https://www.youtube.com/watch?v=ReHwNtoRMrY
A video bringing the quadratic formula to life.