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### Course: Algebra 1>Unit 14

Lesson 1: Intro to parabolas

# 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?
• 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]
• If a parabola has a zero in the equation what happens from there, is there a solution to the problem?
• 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.
• @ 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.
• how do U know whether it is up or down parabola
• 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.
• I don’t really understand why the y value is 60.
• 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.
• 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?