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:

Intuiting

The act of understanding or knowing something immediately without the need for conscious reasoning, often seen as an instinctual or gut feeling.

Sensing

The process of receiving information through the senses, such as sight, hearing, touch, taste, and smell.

Imagining

The mental action or process of forming new ideas, sensations, or concepts not present to the senses.

Thinking

The process of considering or reasoning about something; the cognitive process involved in forming a new concept or idea.