Algebra II - Parabolas Flashcards

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?

x = (1/4p)y^2 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, 0) Signup and view all the answers

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

x = -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?

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

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

(h, k + 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?

y = k - 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?

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

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

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

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

x = h - p Signup and view all the answers

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

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

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

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

How do you write a quadratic equation given three points?

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

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

The graph is narrower Signup and view all the answers

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

The graph is wider 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.

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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.