Find the Vertex, Focus, and Directrix of the Parabola $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$

question 453

Multiple Choice

Find the vertex, focus, and directrix of the parabola. $\left( x + \frac { 7 } { 2 } \right) ^ { 2 } = 4 ( y - 1 )$

• A)Vertex: \(\left( - \frac { 7 } { 2 } , 1 \right)\) ; Focus: \(\left( - \frac { 7 } { 2 } , 2 \right)\) ; Directrix: \(y = 0\)
• B)Vertex: \(\left( - \frac { 7 } { 2 } , 2 \right)\) ; Focus: \(\left( - \frac { 7 } { 2 } , 2 \right)\) ; Directrix: \(y = 1\)
• C)Vertex: \(\left( - \frac { 7 } { 2 } , 2 \right)\) ; Focus: \(\left( - \frac { 7 } { 2 } , 1 \right)\) ; Directrix: \(y = 0\)
• D)Vertex: \(\left( - \frac { 7 } { 2 } , 1 \right)\) ; Focus: \(\left( - \frac { 7 } { 2 } , 2 \right)\) ; Directrix: \(y = 1\)
• E)Vertex: \(\left( - \frac { 7 } { 2 } , 1 \right)\) ; Focus: \(\left( - \frac { 7 } { 2 } , 1 \right)\) ; Directrix: \(y = 1\)

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Definitions:

Limited Resources

A situation in an ecosystem where the availability of resources such as food, water, or territory is insufficient to fulfill the needs of all organisms competing for them.

Consumption Overpopulation

A situation where the level of consumption by a population exceeds the ecosystem's carrying capacity, leading to environmental degradation.

Interference Competition

A form of competition where individuals directly interact and inhibit each other's access to resources, often through aggressive or exclusionary behavior.

Exploitation Competition

An interaction between organisms in which one species reduces the availability or quality of a resource as it uses it, negatively affecting another species' access to the resource.