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## Algebra 1

# 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?(12 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](12 votes)

- If a parabola has a zero in the equation what happens from there, is there a solution to the problem?(6 votes)
- how do U know whether it is up or down parabola(5 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 don’t really understand why the y value is 60.0:57(2 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.(3 votes)

- I Don't know how to graph it dosent make since to me can someone help me.(3 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)
- 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)

- 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)
- 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.(4 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.(4 votes)

- How do you identify each point from the parabola ??(1 vote)
- 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.(3 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.