Write the Function in the Form $f ( x ) = a ( x - h ) ^ { 2 } + k$

question 19

Multiple Choice

Write the function in the form $f ( x ) = a ( x - h ) ^ { 2 } + k$ by completing the square.
$$g ( x ) = - 3 x ^ { 2 } + 15 x + 2$$

• A) \(g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 217 } { 12 }\)
• B) \(g ( x ) = - 3 ( x + 15 ) ^ { 2 } + 2\)
• C) \(g ( x ) = - 3 \left( x - \frac { 5 } { 2 } \right) ^ { 2 } + \frac { 83 } { 4 }\)
• D) \(g ( x ) = - 3 ( x + 5 ) ^ { 2 } - \frac { 2 } { 3 }\)

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Definitions:

Neuroticism

A personality trait characterized by emotional instability, anxiety, moodiness, worry, and sadness.

Unpleasant Emotions

Feelings that are typically described as negative such as sadness, anger, fear, or disgust, which are often a response to undesirable experiences or thoughts.

Standardized Test

A test designed to be administered and scored in a consistent, or "standard," manner, widely used to compare the abilities or knowledge of individuals across various domains.

Known Distribution

A statistical term referring to a distribution whose properties (such as mean and variance) are known.