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# Interpreting a parabola in context

Given a parabola that models a context, we can relate key features of the parabola — like the y-intercept, vertex, and x-intercepts — to what they represent in the given context. Created by Sal Khan.

## Want to join the conversation?

- Can someone just explain what parabola means in a very concise but understanding way?(18 votes)
- A parabola is a plane curve, mostly U-shaped (and a symmetrical open figure), which has a center at the very bottom or top, with one side mirroring/reflecting the other.

(More detail below)

In other words, when starting at the bottom or top of the parabola, the vertical distance reached for traveling toward the left will be the same vertical distance reached on the other side.

The graph Sal Khan uses has a center at the very top, (10, 80). Going toward the left by 10 gives (0, 60), and toward the right has (20, 60); both spots have a height (y-value) of 60.

Sal Khan has said negative periods of time cannot be considered real here, but note how the pattern goes for the entire graph--going toward either the right or left by 20 from the center both will reach a height of 0 on the graph.

[R](22 votes)

- If a parabola has a zero in the equation what happens from there, is there a solution to the problem?(7 votes)
- It depends on where the 0 is situated(1 vote)

- I Don't know how to graph it dosent make since to me can someone help me.(4 votes)
- @ Evan Cole;

This is a very good question. Please note that the question says; the drone is launched from 60 meter above the ground so at zero second the drone is already 60 meters above the ground. However mathematically a parabola is a symmetric graph. In this particular graph based on its equation you have two x-intercepts which are at (-10) and 30 . The positive intercept makes sense to most since time is always positive and since the y- intercept at 30, is zero, people understand that the drone landed on the ground after 30 seconds. It is the (-10 seconds) that is a bit confusing. The interpretation of it is actually very simple! If the person who is operating the drone would not have gone on the cliff to launch it and stayed on the ground then the time for the drone to reach its maximum height of 80 meters would be TEN SECOND longer, since they are now on the ground and the drone has to travel 60 meters higher to reach the cliff from the ground and then reach its maximum height of 80 meters.

I hope this explanation is helpful.(4 votes) - how do U know whether it is up or down parabola(4 votes)
- if it's an upwards parabola it's from top to bottom to up, like a U.If it's a downwards parabola it's the opposite from down to up to down, like an upside down U.(1 vote)

- I just wanted to make sure I understand the solution correctly:

1. The height of the platform. From the texts, "the drone off of a platform" so the 0 second starts from the platform, and it's at y=60 meters.

2. The drone's maximum height is the vertex of the parabola or y=80 meters.

3. The time when the drone landed on the ground is in the x-intercept or x=30 seconds.(3 votes) - I don’t really understand why the y value is 60.0:57(4 votes)
- A parabola is a plane curve, mostly U-shaped (and a symmetrical open figure), which has a center at the very bottom or top, with one side mirroring/reflecting the other.

(More detail below)

In other words, when starting at the bottom or top of the parabola, the vertical distance reached for traveling toward the left will be the same vertical distance reached on the other side.

The graph Sal Khan uses has a center at the very top, (10, 80). Going toward the left by 10 gives (0, 60), and toward the right has (20, 60); both spots have a height (y-value) of 60.

Sal Khan has said negative periods of time cannot be considered real here, but note how the pattern goes for the entire graph--going toward either the right or left by 20 from the center both will reach a height of 0 on the graph.(0 votes)

- In the questions, they asked questions like "Sophie opens a new restaurant. The function "f" models the restaurant's net worth (in thousands of dollars) as a function of time (in months) after Sophie opens it." but they don't give the amount of time that has passed since Sophie has opened the restaurant. How do you solve these kind of questions?(3 votes)
- How do you do this?(1 vote)
- I was also confused until I watched the video more carefully. Look at the labels for the x and y axes: height and seconds. If the drone took off at the x coordinate 0 seconds, find where the graph has a y value (a height) that intersects with 0 seconds. This y value appears to be 60, so the height of the platform/ when the drone took off was 60 meters.(5 votes)

- Why does the line look like that?(1 vote)
- It's not a line. It's a parabola. It looks like that because the outputs don't linearly increase (which would give a line). They increase at an exponential rate.(5 votes)

## Video 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.