Identify the Vertex, Axis of Symmetry, and Intercepts for the Graph

question 162

Multiple Choice

Identify the vertex, axis of symmetry, and intercepts for the graph of the function.
- $$g ( x ) = - x ^ { 2 } + 6 x - 11$$

• A) Vertex at \(( - 3 , - 38 )\); axis: \(x = - 3 ; x\)-intercepts: \(( 3 - \sqrt { 2 } , 0 )\) and \(( 3 + \sqrt { 2 } , 0 ) ; y\)-intercept: \(( 0 , - 11 )\)
• B) Vertex at \(( - 3 , - 38 )\); axis: \(y = - 38 ; x\)-intercepts: none; \(y\)-intercept: \(( 0,11 )\)
• C) Vertex at \(( 3 , - 2 )\); axis: \(y = - 2 ; x\)-intercepts: \(( 3 - \sqrt { 2 } , 0 )\) and \(( 3 + \sqrt { 2 } , 0 ) ; y\)-intercept: \(( 0,11 )\)
• D) Vertex at \(( 3 , - 2 )\); axis: \(x = 3 ; x\)-intercepts: none; \(y\)-intercept: \(( 0 , - 11 )\)

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Definitions:

Laziness

A lack of willingness to act or exert effort, often resulting in inactivity or avoidance of work.

Thrifty Metabolism

A theory suggesting some individuals' bodies are more efficient at storing fat and using energy, historically advantageous but now possibly linked to obesity.

Food Shortages

Situations where the supply of food is insufficient to meet the demand, often resulting in hunger, malnutrition, and social unrest.

Set-Point

A theory suggesting that the body naturally maintains a certain weight by regulating feelings of hunger and metabolism.