About this video
Using a graph of a drone's height over time, the video identifies the point showing the platform height (60 m at t = 0), the maximum height (80 m at 10 seconds) and the landing time (30 seconds). It explains why the zero at t = -10 doesn't make sense, so the domain should be restricted to non-negative times.
You'll be able to
- find the starting value of a real-world quadratic from its graph.
- read the maximum point of a parabola and explain what it means in context.
- find when a modelled height reaches zero and decide which zeros make sense.
Key words
- Model
- A function used to describe a real situation, like the drone's height over time.
- Maximum height
- The highest point on the graph, at the vertex of a downward-opening parabola.
- Domain
- The input values that make sense for a function; here, times from t = 0 onward.
Transcript
- [Instructor] 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, and, 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. So the drone is at the height of the platform right when it takes off, 'cause it says Adam flew his remote controlled 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. So that point right over there tells us the height of the platform. And 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. So then as time goes on, we can see the drone starts going to a higher and higher and higher height, gets as high as 80 meters. And then it starts going down. So it looks like 80 meters, at time 10 seconds, the drone hits a maximum height of 80 meters.
And then last 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, and we can see that that happens right over here. And that happens at time t equals 30 seconds.
And so we've just marked it off, and I know what some of you all are thinking. Wait, there's another time where the drone's height is at zero, and that's right over here. That's at negative 10 seconds. Couldn't we say that that's also a time when the drone landed on the ground?
And this is a important point to realize, because 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, it actually, we would probably want to restrict its domain to positive times.
And 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 thins.
Video © Khan Academy, used under CC BY-NC-SA. Watch on Khan Academy. Puzzicle is not affiliated with Khan Academy.