This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.
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Desmos Graphing: Easy Parabolas and Quadratic Equations for Kids!
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Understanding Parabola Equations
This page introduces the fundamental components of parabolas and their equations. It covers both vertically and horizontally oriented parabolas, emphasizing the relationship between the equation form and the parabola's orientation.
For vertically oriented parabolas (y-axis symmetry), the standard form is x² = 4py, where p determines the distance from the vertex to the focus and directrix. The focus is located at (0, p) and the directrix at y = -p.
For horizontally oriented parabolas (x-axis symmetry), the equation takes the form y² = 4px. Here, the focus is at (p, 0) and the directrix is x = -p.
Vocabulary: Vertex - The point where a parabola changes direction, often the highest or lowest point.
Definition: Directrix - A line perpendicular to the axis of symmetry of a parabola, used in defining the parabola.
Highlight: The value of p in the equation determines whether the parabola opens upward/rightward (p > 0) or downward/leftward (p < 0).
The page also presents variations of these equations for parabolas with different orientations and openings, providing a comprehensive overview of parabola equation forms.
Quadratics and parabolas are fundamental concepts in algebra, with wide-ranging applications in mathematics and physics. This guide provides a comprehensive overview of parabola equations, focusing on their key components and how to derive them from graphs.
- The guide covers different forms of parabola equations, including those with vertical and horizontal axes of symmetry.
- It explains crucial elements such as the vertex, focus, and directrix of parabolas.
- Examples are provided to illustrate how to write parabola equations from given information or graphs.
- The relationship between the focus, directrix, and the equation of a parabola is thoroughly explored.
Deriving Parabola Equations from Graphs
This page demonstrates how to derive a parabola equation from a given graph or set of information. It presents an example of a horizontally oriented parabola.
The example shows a parabola with its vertex at (0, 0) and focus at (-2, 0). The directrix is located at x = 2.
Example: For a parabola with focus at (-2, 0) and directrix at x = 2, the equation is derived as y² = -8x.
The process of deriving the equation involves:
- Identifying the orientation of the parabola (horizontal in this case).
- Locating the focus and directrix.
- Applying the general formula y² = 4px, where p is the distance from the vertex to the focus.
- Calculating p as -2 (negative because the parabola opens to the left).
Highlight: The axis of symmetry for this parabola is y = 0, which is consistent with its horizontal orientation.
This example illustrates the practical application of parabola equation formulas and demonstrates how to use a parabola graph calculator conceptually.
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Desmos Graphing: Easy Parabolas and Quadratic Equations for Kids!
This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.
Understanding Parabola Equations
This page introduces the fundamental components of parabolas and their equations. It covers both vertically and horizontally oriented parabolas, emphasizing the relationship between the equation form and the parabola's orientation.
For vertically oriented parabolas (y-axis symmetry), the standard form is x² = 4py, where p determines the distance from the vertex to the focus and directrix. The focus is located at (0, p) and the directrix at y = -p.
For horizontally oriented parabolas (x-axis symmetry), the equation takes the form y² = 4px. Here, the focus is at (p, 0) and the directrix is x = -p.
Vocabulary: Vertex - The point where a parabola changes direction, often the highest or lowest point.
Definition: Directrix - A line perpendicular to the axis of symmetry of a parabola, used in defining the parabola.
Highlight: The value of p in the equation determines whether the parabola opens upward/rightward (p > 0) or downward/leftward (p < 0).
The page also presents variations of these equations for parabolas with different orientations and openings, providing a comprehensive overview of parabola equation forms.
Quadratics and parabolas are fundamental concepts in algebra, with wide-ranging applications in mathematics and physics. This guide provides a comprehensive overview of parabola equations, focusing on their key components and how to derive them from graphs.
- The guide covers different forms of parabola equations, including those with vertical and horizontal axes of symmetry.
- It explains crucial elements such as the vertex, focus, and directrix of parabolas.
- Examples are provided to illustrate how to write parabola equations from given information or graphs.
- The relationship between the focus, directrix, and the equation of a parabola is thoroughly explored.
Deriving Parabola Equations from Graphs
This page demonstrates how to derive a parabola equation from a given graph or set of information. It presents an example of a horizontally oriented parabola.
The example shows a parabola with its vertex at (0, 0) and focus at (-2, 0). The directrix is located at x = 2.
Example: For a parabola with focus at (-2, 0) and directrix at x = 2, the equation is derived as y² = -8x.
The process of deriving the equation involves:
- Identifying the orientation of the parabola (horizontal in this case).
- Locating the focus and directrix.
- Applying the general formula y² = 4px, where p is the distance from the vertex to the focus.
- Calculating p as -2 (negative because the parabola opens to the left).
Highlight: The axis of symmetry for this parabola is y = 0, which is consistent with its horizontal orientation.
This example illustrates the practical application of parabola equation formulas and demonstrates how to use a parabola graph calculator conceptually.
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Can't find what you're looking for? Explore other subjects.
Knowunity is the # 1 ranked education app in five European countries
Knowunity was a featured story by Apple and has consistently topped the app store charts within the education category in Germany, Italy, Poland, Switzerland and United Kingdom. Join Knowunity today and help millions of students around the world.
4.9+
Average App Rating
13 M
Students use Knowunity
#1
In Education App Charts in 12 Countries
950 K+
Students uploaded study notes
Still not sure? Look at what your fellow peers are saying...
iOS User
I love this app so much [...] I recommend Knowunity to everyone!!! I went from a C to an A with it :D
Stefan S, iOS User
The application is very simple and well designed. So far I have found what I was looking for :D
SuSSan, iOS User