Algebra II - Parabolas Flashcards
17 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is the standard equation for a parabola with its vertex at the origin and a vertical axis of symmetry?

  • x = (1/4p)y^2
  • y = a(x - h)^2 + k
  • x = (1/4p)(y - k)^2 + h
  • y = (1/4p)x^2 (correct)
  • 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?

    <p>x = (1/4p)y^2</p> Signup and view all the answers

    What is the focus of a standard parabola with vertex at the origin and horizontal axis of symmetry?

    <p>(p, 0)</p> Signup and view all the answers

    What is the directrix of a standard parabola with vertex at the origin and horizontal axis of symmetry?

    <p>x = -p</p> Signup and view all the answers

    What is the standard equation for a parabola with vertex at (h, k) and a vertical axis of symmetry?

    <p>y = (1/4p)(x - h)^2 + k</p> Signup and view all the answers

    What is the focus of a standard parabola with vertex at (h, k) and vertical axis of symmetry?

    <p>(h, k + p)</p> Signup and view all the answers

    What is the directrix of a standard parabola with vertex at (h, k) and vertical axis of symmetry?

    <p>y = k - p</p> Signup and view all the answers

    What is the standard equation for a parabola with vertex at (h, k) and a horizontal axis of symmetry?

    <p>x = (1/4p)(y - k)^2 + h</p> Signup and view all the answers

    What is the focus of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?

    <p>(h + p, k)</p> Signup and view all the answers

    What is the directrix of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?

    <p>x = h - p</p> Signup and view all the answers

    What is the vertex form of a quadratic equation when given the vertex (h, k)?

    <p>y = a(x - h)^2 + k</p> Signup and view all the answers

    What is the intercept form of a quadratic equation when given the x-intercepts p and q?

    <p>y = a(x - p)(x - q)</p> Signup and view all the answers

    How do you write a quadratic equation given three points?

    <p>Write/Solve system of three equations</p> Signup and view all the answers

    What happens to the graph of a quadratic equation when |a| > 1?

    <p>The graph is narrower</p> Signup and view all the answers

    What happens to the graph of a quadratic equation when |a| < 1?

    <p>The graph is wider</p> Signup and view all the answers

    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.

    Studying That Suits You

    Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

    Quiz Team

    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.

    More Like This

    Use Quizgecko on...
    Browser
    Browser