An Equation of a Parabola Is Given $$x ^ { 2 } - 8 x - 16 y - 16 = 0$$

question 14

Multiple Choice

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
vertex and the focus.
- $$x ^ { 2 } - 8 x - 16 y - 16 = 0$$

• A) \(( x - 4 ) ^ { 2 } = 16 ( y + 2 )\)
• vertex: \(( - 2,4 )\); focus \(( 2,4 )\)
• B) \(( x - 4 ) ^ { 2 } = 16 ( y + 2 )\)
• vertex: \(( - 4,2 )\); focus \(( - 4,6 )\)
• C) \(( x + 4 ) ^ { 2 } = 16 ( y - 2 )\)
• vertex: \(( - 4,2 )\); focus \(( - 4,6 )\)
• D) \(( x - 4 ) ^ { 2 } = 16 ( y + 2 )\)
• vertex: \(( 4 , - 2 )\); focus \(( 4,2 )\)

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Definitions:

Potential Output

The highest level of economic output an economy can sustain over the long term without increasing inflation, determined by available resources and technology.

Aggregate Demand

The sum total of desires for products and services within an economic entity, marked at a specific price level through a chosen timeframe.

Expansionary Gap

Occurs when an economy's actual output is higher than the potential output, often leading to higher inflation.

Active Approach

A management strategy where decisions are made using discretionary methods to try to outperform the market or a specific benchmark.