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

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.