yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

Interpreting a parabola in context | Quadratic functions & equations | Algebra I | Khan Academy


2m read
·Nov 10, 2024

We're told that Adam flew his remote controlled drone off of a platform. The function f models the height of the drone above the ground in meters as a function of time in seconds after takeoff. So, what they want us to do is plot the point on the graph of f that corresponds to each of the following things.

So pause the video and see if you can do that. Obviously, you can't draw on your screen. This is from an exercise on Khan Academy, but you can visually look at it and even with your finger point to the part of the graph of f that represents each of these things.

All right, so the first thing here is the height of the platform. The drone is at the height of the platform right when it takes off because it says Adam flew his remote control drone off of a platform. So what is the time that he's taking off the drone, or the drone is taking off? Well, that's going to be at time t equals zero, right over here.

And what is the height of the drone at that moment? It is 60 meters. So that must be the height of the platform. That point right over there tells us the height of the platform. If they asked us what the height of the platform is, it would be 60 meters.

The next one is the drone's maximum height. As time goes on, we can see the drone starts going to a higher and higher and higher height and gets as high as 80 meters. Then it starts going down. So it looks like at 80 meters, at time 10 seconds, the drone hits a maximum height of 80 meters.

Lastly, but not least, they say the time when the drone landed on the ground. Now we can assume that the ground is when the height of the drone is at zero meters. We can see that this happens right over here and that happens at time t equals 30 seconds.

So we've just marked it off. I know some of y'all are thinking, "Wait, there's another time where the drone's height is at zero." That's right, over here at negative 10 seconds. Couldn't we say that that's also a time when the drone landed on the ground?

This is an important point to realize. If we're really trying to model the drone's behavior from time t equals zero, if t equals zero is right when you take off all the way to it lands, then this parabola that we're showing right over here, we would probably want to restrict its domain to positive times.

So this negative time region right over here really doesn't make a lot of sense. We should probably consider the non-negative values of time when we're trying to think about these different things.

More Articles

View All
How this 96-year-old Secretary grew a $9,000,000 Fortune
What’s up you guys? It’s Graham here. So, I want to share a really cool story written by Corey Kildonan of the New York Times. It’s a great example of what can happen when you live frugally and invest consistently while still working a very modest nine-to…
You Don't Need Dopamine Detox
If you’re watching this video on your phone, chances are that before I’m done talking, you’ll get a notification, a text from a friend, a like on a recent post you just shared, or a new follower or subscriber. When this happens, do you feel a rush, a sens…
"EMPATHY" - другой взгляд на теннис
Hello, dear friends! Today I would like to make a video illustration of the word “empathy.” This word has a literal translation as compassion, sympathy. But in fact, the most important translation of this word is to understand the situation from the other…
Daily Live Homeroom With Sal: Monday, April 13
Hi everyone! Sal Khan here. Welcome to our daily homeroom livestream. As I always explain, this is a way for us to stay together, connected in this time of school closures. Khan Academy, we’re not-for-profit, with a mission of providing a free, world-clas…
Paralysed Rats Made To Walk Again
We have all heard of mind over matter, but is it possible that the right motivation can actually help repair spinal damage? I have come to Lausanne, Switzerland, to find out about some innovative research being done to repair the spinal cords of rats usin…
Get to Know Your Land | Live Free or Die: How to Homestead
[Music] [Music] Hello there! Well, hello there! We’re hanging out in the forest garden, being cool homesteaders. So, when I first came here, I had this idea from looking at pictures and books of what my homestead was going to look like; pictures that we…