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## Algebra 1

### 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?
• 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 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.
• I Don't know how to graph it dosent make since to me can someone help me.
• 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?
• 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.
• 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.