<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation
Our Terms of Use (click here to view) and Privacy Policy (click here to view) have changed. By continuing to use this site, you are agreeing to our new Terms of Use and Privacy Policy.

Use Graphs to Solve Quadratic Equations

Identify x-intercepts of parabolas

Atoms Practice
Estimated10 minsto complete
%
Progress
Practice Use Graphs to Solve Quadratic Equations
Practice
Progress
Estimated10 minsto complete
%
Practice Now
Roller Coaster Relationships

Credit: Rene Schwietzke
Source: http://www.flickr.com/photos/rene-germany/18978653/
License: CC BY-NC 3.0

Have you ever ridden a roller coaster? The people who design these rides need a deep understanding of math and physics. They have to calculate how big to make the hills, how fast the roller coaster will move at various points on the track, and how long the ride should last. The equation at the very heart of all these calculations is a quadratic equation.

One Equation to Rule Them All

When a roller coaster designer needs to make calculations, she starts with a very basic formula:

\begin{align*}\text{distance}=\text{(initial velocity)(time)}+\frac{1}{2}\text{(acceleration)(time)}^2\end{align*}

This is a quadratic equation, with time as the variable. The equation allows her to figure out how far the roller coaster train can travel once it starts down the first hill. Using this equation, the designer can also calculate when the coaster will hit its top speed and what that speed will be. It provides a starting point for understanding how the coaster will behave on climbs and at turns, and whether it can arrive safely back at the station.

Credit: flatluigi
Source: http://www.flickr.com/photos/flatluigi/1270871046/
License: CC BY-NC 3.0

Designers have to make sure their coasters are safe long before construction begins. Coasters are expensive to build, so designers have to verify that their proposed ride will balance safety and thrills before it's made into reality. Yet, even with all of these precautions, roller coasters still carry some risk.

See for yourself: http://www.nbcnews.com/video/nightly-news/52538877#52538877

Explore More

Check out the links below to learn more about how roller coasters use math and physics to deliver a thrill.

http://www.nytimes.com/2012/07/03/science/wood-takes-a-thrilling-turn-in-roller-coaster-design.html

http://www.youtube.com/watch?v=cao4JSfaA7s

http://www.youtube.com/watch?v=K36iWnSaOEQ

Image Attributions

  1. [1]^ Credit: Rene Schwietzke; Source: http://www.flickr.com/photos/rene-germany/18978653/; License: CC BY-NC 3.0
  2. [2]^ Credit: flatluigi; Source: http://www.flickr.com/photos/flatluigi/1270871046/; License: CC BY-NC 3.0

Explore More

Sign in to explore more, including practice questions and solutions for Use Graphs to Solve Quadratic Equations.
Please wait...
Please wait...