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
Facebook Freebooting - Smarter Every Day 128
Hey, it’s me Destin. Welcome back to Smarter Every Day. I want to do something a little bit different today; let’s start with a story. Once there was a kingdom where wealth was determined by what sheep you owned. There was a rich man who had many, many s…
TAOISM | The Power of Letting Go
Mastery of the world is achieved by letting things take their natural course. You can not master the world by changing the natural way. Lao Tzu Our civilization is in a state of ongoing strivings, in which control seems to be the highest virtue. We don’…
Poor Visibility and Cold Fingers | Life Below Zero
With her loader on its way to Kavik, Sue attempted to meet the convoy to guide them to camp safely. However, dangerous conditions forced her to return home. Checking on the status and safety of the delivery crew is a priority. “Hack, a cold! I mean, comi…
Variance and standard deviation of a discrete random variable | AP Statistics | Khan Academy
In a previous video, we defined this random variable (X). It’s a discrete random variable; it can only take on a finite number of values. I defined it as the number of workouts I might do in a week. We calculated the expected value of our random variable …
The 4 Companies That Secretly Control the World
Tim Cook of Apple, Sundar Pichai of Google, Elon Musk, Jeff Bezos, the president of the United States - when you think of the people controlling the world, these names come to mind. But the truth is, while these people have a significant influence over ou…
Butchering a Goat in Africa - Smarter Every Day 34
Hey, it’s me Destin. Welcome to Smarter Every Day. So, this video contains real world stuff, so no little eyes or no little ears. When my sister cooks in Africa, she can’t do what I just did. She can’t go to the fridge and just pull out a pound of ground …