Find the Vertex, Focus, and Directrix of the Parabola $y = - \frac { 1 } { 2 } ( x + 1 ) ^ { 2 }$

question 86

Essay

Find the vertex, focus, and directrix of the parabola $y = - \frac { 1 } { 2 } ( x + 1 ) ^ { 2 }$ , and sketch its graph.

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Definitions:

Prototype

A mental image or best example of a category. Matching new items to a prototype provides a quick and easy method for sorting items into categories (as when comparing feathered creatures to a prototypical bird, such as a crow).

Category

A class or division of people or things regarded as having particular shared characteristics.

Mental Grouping

The cognitive process of categorizing objects or information based on shared attributes or relations, aiding in understanding and memory.

Prototype

An original model or first form from which other forms are copied or developed.