Find the Vertex, Focus, and Directrix of the Parabola $$( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$$

question 51

Multiple Choice

Find the vertex, focus, and directrix of the parabola. Graph the equation.
- $$( y + 1 ) ^ { 2 } = - 8 ( x + 2 )$$

• A) vertex: \( (1,2) \) focus: \( (-1,2) \) directrix: \( x=3 \)
• B) vertex: \( (-2,-1) \) focus: \( (-2,-3) \) directrix: \( y=1 \)
• C) vertex: \( (2,1) \) focus: \( (2,-1) \) directrix: \( y=3 \)
• D) vertex: \( (-2,-1) \) focus: \( (-4,-1) \) directrix: \( x=0 \)

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Definitions:

Trans-hex-3-ene

A geometric isomer of hex-3-ene with the two substituents opposite to each other across the double bond, affecting its chemical properties and reactivity.

Major Organic Product

The primary product of an organic reaction, usually the one in greater yield when multiple products are possible.

Major Organic Product

The primary product obtained in the largest quantity from an organic reaction, considering the reaction's mechanism and conditions.

Alkenes

Hydrocarbons that contain at least one double bond between carbon atoms, characterized by the formula CnH2n.