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This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.
2/13/2023
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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.
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:
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.
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.
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This parabola opens upward with vertex at (0, 0) and focus at (0, 2). The directrix is y = -2. The equation is x² = 8y.
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.
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:
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.
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.
Algebra 2 - parabolas (algebra 2) (condensed)
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List of all necessary formulas that need to be known and/or memorized for integrated mathematics 3/algebra 2 curriculum.
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Graph and write equations of a circle
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Algebra 2 - The Quadratic Formula
Examples of solving the quadratic formula.
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Average App Rating
Students use Knowunity
In Education App Charts in 12 Countries
Students uploaded study notes
iOS User
Stefan S, iOS User
SuSSan, iOS User
