Is x=y^2-6 y+3 an equation for a parabola? Explain. |...

Name: Problem 132, Chapter 10: Intermediate Algebra for College Students
Uploaded: 2019-08-12T18:13:03-08:00
Duration: 35 s
Channel: Adam Dehollander
Description: Is x=y^2-6 y+3 an equation for a parabola? Explain.

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Key Concepts

Equation Transformation (Completing the Square)

Completing the square is a method used to rewrite a quadratic equation in its vertex form. This transformation helps in easily determining the vertex, axis of symmetry, and the direction in which the parabola opens, thereby confirming the curve as a parabola.

Conic Sections

Conic sections are the curves produced by the intersection of a plane and a cone. They include circles, ellipses, parabolas, and hyperbolas. Each of these curves has a general quadratic equation form, and recognizing a parabola among them involves identifying the presence of a single squared variable.

Parabola

A parabola is a conic section defined by an equation that includes a squared term. Its characteristic property is that every point on the curve is equidistant from a fixed point (the focus) and a fixed straight line (the directrix). The orientation of the parabola (opening upward, downward, leftward, or rightward) is determined by whether the squared term is in x or y.

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