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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 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?
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?
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?
What is the standard equation for a parabola with its vertex at the origin and a horizontal axis of symmetry?
What is the focus of a standard parabola with vertex at the origin and horizontal axis of symmetry?
What is the focus of a standard parabola with vertex at the origin and horizontal axis of symmetry?
What is the directrix of a standard parabola with vertex at the origin and horizontal axis of symmetry?
What is the directrix of a standard parabola with vertex at the origin and horizontal axis of symmetry?
What is the standard equation for a parabola with vertex at (h, k) and a vertical axis of symmetry?
What is the standard equation for a parabola with vertex at (h, k) and a vertical axis of symmetry?
What is the focus of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
What is the focus of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
What is the directrix of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
What is the directrix of a standard parabola with vertex at (h, k) and vertical axis of symmetry?
What is the standard equation for a parabola with vertex at (h, k) and a horizontal axis of symmetry?
What is the standard equation for a parabola with vertex at (h, k) and a horizontal axis of symmetry?
What is the focus of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
What is the focus of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
What is the directrix of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
What is the directrix of a standard parabola with vertex at (h, k) and horizontal axis of symmetry?
What is the vertex form of a quadratic equation when given the vertex (h, k)?
What is the vertex form of a quadratic equation when given the vertex (h, k)?
What is the intercept form of a quadratic equation when given the x-intercepts p and q?
What is the intercept form of a quadratic equation when given the x-intercepts p and q?
How do you write a quadratic equation given three points?
How do you write a quadratic equation given three points?
What happens to the graph of a quadratic equation when |a| > 1?
What happens to the graph of a quadratic equation when |a| > 1?
What happens to the graph of a quadratic equation when |a| < 1?
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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