Table of contents
- 0. Review of Algebra4h 16m
- 1. Equations & Inequalities3h 18m
- 2. Graphs of Equations43m
- 3. Functions2h 17m
- 4. Polynomial Functions1h 44m
- 5. Rational Functions1h 23m
- 6. Exponential & Logarithmic Functions2h 28m
- 7. Systems of Equations & Matrices4h 6m
- 8. Conic Sections2h 23m
- 9. Sequences, Series, & Induction1h 19m
- 10. Combinatorics & Probability1h 45m
8. Conic Sections
Parabolas
7:08 minutes
Problem 23a
Textbook Question
Textbook QuestionIn Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. Focus: (0, - 25); Directrix: y = 25
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Key Concepts
Here are the essential concepts you must grasp in order to answer the question correctly.
Standard Form of a Parabola
The standard form of a parabola that opens vertically is given by the equation (x - h)² = 4p(y - k), where (h, k) is the vertex and p is the distance from the vertex to the focus or directrix. This form allows for easy identification of the parabola's orientation and key features.
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Parabolas as Conic Sections
Focus and Directrix
In the context of parabolas, the focus is a fixed point from which distances to points on the parabola are measured, while the directrix is a line that is equidistant from the focus. The parabola is defined as the set of all points that are equidistant from the focus and the directrix, which is crucial for determining its equation.
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Parabolas as Conic Sections
Vertex of a Parabola
The vertex of a parabola is the point where it changes direction and is located midway between the focus and the directrix. For the given conditions, the vertex can be calculated as the midpoint of the focus and the directrix, which is essential for writing the standard form of the parabola's equation.
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Horizontal Parabolas
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