Questions and Answers
What is the standard equation for a parabola with its vertex at the origin and a vertical axis of symmetry?
What is the focus of a standard parabola with vertex at the origin and vertical axis of symmetry?
(0, p)
What is the directrix of a standard parabola with vertex at the origin and vertical axis of symmetry?
y = -p
What is the standard equation for a parabola with its vertex at the origin and a horizontal axis of symmetry?
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What is the focus of a standard parabola with vertex at the origin and horizontal axis of symmetry?
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What is the directrix of a standard parabola with vertex at the origin and horizontal axis of symmetry?
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What is the standard equation for a parabola with vertex at (h, k) and a vertical axis of symmetry?
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What is the focus of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
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What is the directrix of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
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What is the standard equation for a parabola with vertex at (h, k) and a horizontal axis of symmetry?
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What is the focus of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
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What is the directrix of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
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What is the vertex form of a quadratic equation when given the vertex (h, k)?
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What is the intercept form of a quadratic equation when given the x-intercepts p and q?
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How do you write a quadratic equation given three points?
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What happens to the graph of a quadratic equation when |a| > 1?
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What happens to the graph of a quadratic equation when |a| < 1?
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Study Notes
Standard Equations at the Origin
- Vertical Axis of Symmetry: Equation is y = (1/4p)x², focus at (0, p), directrix y = -p.
- Horizontal Axis of Symmetry: Equation is x = (1/4p)y², focus at (p, 0), directrix x = -p.
Standard Equations with Vertex
- With Vertical Axis: Equation is y = (1/4p)(x - h)² + k, focus at (h, k + p), directrix y = k - p.
- With Horizontal Axis: Equation is x = (1/4p)(y - k)² + h, focus at (h + p, k), directrix x = h - p.
Writing Quadratic Equations
- Given Vertex (h, k): Use Vertex Form y = a(x - h)² + k.
- Given X-intercepts (p, q): Use Intercept Form y = a(x - p)(x - q).
- Given Three Points: Formulate and solve a system of three equations to determine the quadratic equation.
Standard Form Characteristics
- When |a| > 1: Graph is narrower.
- When |a| < 1: Graph is wider.
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Description
Test your understanding of parabolas with these flashcards focusing on standard equations, axes of symmetry, and vertex forms. Each card provides key definitions and equations essential for mastering parabolic concepts in Algebra II.