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:

AVC

AVC stands for Average Variable Costs, referring to the total variable costs of production divided by the quantity of output produced, indicating how variable costs per unit change with output levels.

ATC

The cost per unit of output, calculated by dividing the total costs (both fixed and variable) by the total quantity produced; identical to Average Total Cost.

MC

Marginal Cost; the change in total production cost that arises when the quantity produced is incremented by one unit.

Marginal Cost

The cost of producing one additional unit of a product or service, an important concept in economics for decision-making regarding production levels.