Find the Vertex of the Graph of the Quadratic Function $f ( x ) = x ^ { 2 } - 5 x + 1$

question 122

Multiple Choice

Find the vertex of the graph of the quadratic function. Find any intercepts and graph the function.
- $f ( x ) = x ^ { 2 } - 5 x + 1$

• A) Vertex: \(\left( - \frac { 5 } { 2 } , - 5 \frac { 1 } { 4 } \right)\); \(x\)-intercepts: \(\left( \frac { - 5 \pm \sqrt { 21 } } { 2 } , 0 \right)\) \(y\)-intercept: \(( 0,1 )\)
• B) Vertex: \(( 0,1 )\); \(x\)-intercepts: none; \(\mathrm { y }\)-intercept: \(( 0,1 )\)
• C) Vertex: \(\left( \frac { 5 } { 2 } , - 5 \frac { 1 } { 4 } \right)\); \(x\)-intercepts: \(\left( \frac { 5 \pm \sqrt { 21 } } { 2 } , 0 \right)\) y-intercept: \(( 0,1 )\)
• D) Vertex: \(( 2 , - 9 )\); \(x\)-intercepts: \(( - 1,0 )\) and \(( 5,0 )\); \(y\)-intercept: \(( 0 , - 5 )\)

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Definitions:

Content Effect

Performance variability on reasoning tasks that require identical kinds of formal reasoning but are dissimilar in superficial content.

MAUT

Multi-Attribute Utility Theory, a framework used in decision making to evaluate and compare choices based on multiple criteria.

Inductive Reasoning

A reasoning method where several assumptions, considered true or mostly true, are fused together to derive a particular outcome.

Deductive Reasoning

A logical process in which a conclusion follows necessarily from the stated premises; it is inference where true premises develop a true conclusion.