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
Human fertilization and early development | High school biology | Khan Academy
[Instructor] What we’re gonna do with this video is talk about fertilization and development in human beings, or at least early development in human beings. And this right over here is an actual image of fertilization about to happen or happening. So th…
Behind the scenes: Flying a drone like albatross | Incredible Animal Journeys | National Geographic
Good morning on board the Explorer and greetings from the mud room. They say that size doesn’t matter. Taking enough in three, two, one—here we [Music] go! But in this case, it kind of does. One of the ways we’re reducing risk when flying drones like thi…
What the Fahrenheit?!
As an Australian Canadian, the Fahrenheit temperature scale has always seemed a bit arbitrary to me. I mean, why does water freeze at 32 degrees? Why that integer? And what exactly does 0 represent? According to many sources, the Fahrenheit scale was defi…
npage85: knowing the fundamental character of X
And page 85 made a video called “The Brain Doesn’t Create the Mind.” In it, he tried to use a deductive argument to prove the existence of souls. It went like this: Premise one: All fundamentally same processes create fundamentally same products. Premis…
How Coca Leaves Become Cocaine | Trafficked with Mariana van Zeller
[music playing] [speaking spanish] I’m not going to lie, it’s always a rush getting access to these clandestine worlds. The cocaine pit, the starting point for such a storied black market trade, ranks up there. But as the reporter high wears off, I realiz…
The Man Who Killed Millions and Saved Billions (Clean Version)
The 1918 Nobel Prize for Chemistry is probably the most important Nobel Prize ever awarded. It was given to German scientist Fritz Haber for solving one of the biggest problems humanity has ever faced. His invention is directly responsible for the lives o…