Fill in Each Blank with the Appropriate Response $y = - \frac { 1 } { 6 } ( x + 3 ) ^ { 2 } - 8$

question 106

Multiple Choice

Fill in each blank with the appropriate response.
-The graph of $y = - \frac { 1 } { 6 } ( x + 3 ) ^ { 2 } - 8$ can be obtained from the graph of $y = x ^ { 2 }$ by shifting horizontally $\underline{\quad\quad}$ units to the $\underline{\quad\quad}$ vertically compressing by a factor of $\underline{\quad\quad}$ , reflecting across the $\underline{\quad\quad}$ -axis, and shifting vertically $\underline{\quad\quad}$ units in the $\underline{\quad\quad}$ direction.

• A) \(3 ;\) left; \(\frac { 1 } { 6 } ; x ; 8 ;\) downward
• B) 3 ; right; \(\frac { 1 } { 6 } ; x ; 8 ;\) downward
• C) \(3 ;\) left; \(8 ; x ; \frac { 1 } { 6 } ;\) downward
• D) 3 ; right; \(\frac { 1 } { 6 } ; \mathrm { x } ; 8\); upward

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Definitions:

Projection

A defense mechanism where individuals attribute their own unwanted thoughts, feelings, or motives to another person.

Quarrelsome

Quarrelsome describes a person prone to arguments or disputes, often engaging in hostile exchanges.

Psychoanalytic Theory

is a method of psychology and psychotherapy developed by Sigmund Freud that emphasizes unconscious motives and conflicts.

Inferiority Complex

A psychological condition where an individual feels a deep sense of inadequacy and inferiority, often leading to overcompensation or withdrawal.