If you're seeing this message, it means we're having trouble loading external resources on our website.

If you're behind a web filter, please make sure that the domains *.kastatic.org and *.kasandbox.org are unblocked.

Main content

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?

  • blobby green style avatar for user patluri
    Can someone just explain what parabola means in a very concise but understanding way?
    (10 votes)
    Default Khan Academy avatar avatar for user
    • hopper cool style avatar for user Philip
      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]
      (11 votes)
  • aqualine seed style avatar for user hannahelisewilliams5
    how do U know whether it is up or down parabola
    (4 votes)
    Default Khan Academy avatar avatar for user
  • aqualine seed style avatar for user hannahelisewilliams5
    If a parabola has a zero in the equation what happens from there, is there a solution to the problem?
    (4 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user PAUL Falgout
    I Don't know how to graph it dosent make since to me can someone help me.
    (3 votes)
    Default Khan Academy avatar avatar for user
  • duskpin ultimate style avatar for user <khadija>
    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?
    (2 votes)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user ALDOC
    How do you identify each point from the parabola ??
    (1 vote)
    Default Khan Academy avatar avatar for user
    • piceratops ultimate style avatar for user fr33d0g
      Each point has an x value, and a y value. go to the right or left, wherever your point is, that is its x value. go up or down and that is your y value. with these two coordinates you have an exact point.
      (2 votes)
  • blobby green style avatar for user khlifimanar235
    but after the 30 seconds the graph keeps going down so the remote kept going down
    (1 vote)
    Default Khan Academy avatar avatar for user
  • aqualine ultimate style avatar for user AquamarineWalnut
    Since solving for inequalities is similar to solving for equalities, would I be able to graph an inequality that satisfies the conditions for a parabola? And if so, how?
    (1 vote)
    Default Khan Academy avatar avatar for user
    • mr pink green style avatar for user David Severin
      You noticed the similarities between graphing inequalities in linear functions, so the same would be true of parabolas.
      For linear, we generally graph the y intercept, use the slope to find one or two more good points (as you noted these are the steps of graphing an equality). The last two steps is determine if it is a solid (≥ or ≤) or dashed (< or >) line and graph above (≥ or >) or below (≤ or <) the line assuming you have in slope intercept form.
      The same process would be true for a quadratic funtion (which creates a parabola). Easiest is to find the vertex, find two or more additional points around the vertex which is the same as graphing a quadratic equality. Then, determine if the parabola is solid or dashed just like a linear, and if you should shade above or below the parabola, assuming you have in y= form either standard or vertex form.
      (1 vote)
  • duskpin sapling style avatar for user 94s.skarnakanti
    Can there be a negative time for the landing of the drone?
    (1 vote)
    Default Khan Academy avatar avatar for user
  • blobby green style avatar for user Tatenda2007
    Why is the answer for question 3,30 seconds because when I did it my answer was 10 seconds
    (1 vote)
    Default Khan Academy avatar avatar for user

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.