An Equation of a Parabola Is Given $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

question 122

Multiple Choice

An equation of a parabola is given. Write the equation of the parabola in standard form, and identify the
focus and the equation of the directrix.
- $$4 x ^ { 2 } + 28 x + 40 y + 209 = 0$$

• A) \(\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )\)
• focus: \(\left( - \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;\) directrix \(: y = - \frac { 3 } { 2 }\)
• B) \(( x + 14 ) ^ { 2 } = - 40 \left( y + \frac { 13 } { 40 } \right)\)
• focus: \(\left( - 14 , - \frac { 387 } { 40 } \right) ;\) directrix: \(y = - \frac { 413 } { 40 }\)
• C) \(\left( x - \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y + 4 )\)
• focus: \(\left( \frac { 7 } { 2 } , - \frac { 13 } { 2 } \right) ;\) directrix: \(y = - \frac { 3 } { 2 }\)
• D) \(\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = - 10 ( y - 4 )\)
• focus: \(\left( - \frac { 7 } { 2 } , \frac { 3 } { 2 } \right)\); directrix: \(y = \frac { 13 } { 2 }\)

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Definitions:

Psychodynamic Model

An approach in psychology that emphasizes systematic study of the psychological forces underlying human behavior, feelings, and emotions.

Unconscious Mind

Level of the mind in which thoughts, feelings, memories, and other information are kept that are not easily or voluntarily brought into consciousness.

Biological Model

A theory in psychology that attributes complex phenomena such as mental disorders to biological processes within the body, such as genetic, neurochemical, or brain structure alterations.

Chemical Imbalance

A theory suggesting that mental health conditions are associated with changes in the brain's chemical composition.