An Equation of a Parabola Is Given $$16 y ^ { 2 } - 104 y + 288 x + 1,033 = 0$$

question 57

Multiple Choice

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
vertex and the focus.
- $$16 y ^ { 2 } - 104 y + 288 x + 1,033 = 0$$

• A) \(\left( y - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( x - 3 )\)
• vertex: \(\left( 3 , \frac { 13 } { 4 } \right)\); focus \(\left( - \frac { 15 } { 2 } , \frac { 13 } { 4 } \right)\)
• B) \(\left( y - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( x + 3 )\)
• vertex: \(\left( - 3 , \frac { 13 } { 4 } \right)\); focus \(\left( - \frac { 15 } { 2 } , \frac { 13 } { 4 } \right)\)
• C) \(\left( x + \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( y + 3 )\)
• vertex: \(\left( - \frac { 13 } { 4 } , - 3 \right)\); focus \(\left( - \frac { 13 } { 4 } , - \frac { 15 } { 2 } \right)\)
• D) \(\left( x - \frac { 13 } { 4 } \right) ^ { 2 } = - 18 ( y + 3 )\)
• vertex: \(\left( \frac { 13 } { 4 } , - 3 \right) ;\) focus \(\left( \frac { 13 } { 4 } , - \frac { 15 } { 2 } \right)\)

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Definitions:

Rationalizations

The process of providing reasonable explanations for behaviors, decisions, or business practices that may otherwise appear irrational or unjustified, often to align with societal norms or ethical standards.

Unethical Behaviour

Actions or practices by individuals or organizations that violate moral principles or accepted standards of conduct.

Social Morality

Collective ideas about what is considered right and wrong behavior in society, shaped by cultural, religious, and personal beliefs.

Kohlberg

Refers to Lawrence Kohlberg, an American psychologist best known for his theory of stages of moral development.