Find the Vertex, Focus, and Directrix of the Parabola with the Given

question 39

Multiple Choice

Find the vertex, focus, and directrix of the parabola with the given equation.
- $$( y - 4 ) ^ { 2 } = - 16 ( x - 1 )$$

• A) vertex: \(( 1,4 )\)
• focus: \(( - 3,4 )\)
• directrix: \(x = 5\)
• B) vertex: \(( - 1 , - 4 )\)
• focus: \(( - 5 , - 4 )\)
• directrix: \(x = 3\)
• C) vertex: \(( 1,4 )\)
• focus: \(( 5,4 )\)
• directrix: \(x = - 3\)
• D) vertex: \(( 4,1 )\)
• focus: \(( 0,1 )\)
• directrix: \(x = 8\)

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Definitions:

Tectum

A part of the brain located in the midbrain that plays a role in auditory and visual reflexes.

Basal Ganglia

A group of nuclei in the brain involved in coordinating movement, as well as aspects of learning and memory.

Allocortex

A type of cortical tissue in the brain characterized by fewer layers than the neocortex, involved in functions like emotion and memory.

Hippocampus

A brain structure embedded deep in the temporal lobe, critical for learning and memory.