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:

Exaptation

A trait that becomes used for an entirely new purpose during evolution.

Key Innovation

An evolutionary adaptation that gives its bearer the opportunity to exploit a particular environment more efficiently or in a new way.

Adaptive Radiation

An evolutionary process in which organisms diversify rapidly into a multitude of new forms, particularly when a change in the environment makes new resources available or opens new niches.

Temporal Isolation

A mechanism of reproductive isolation where two species mate or flower at different times, preventing crossbreeding.