Find the Vertex, Focus, and Directrix of the Parabola $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

question 415

Multiple Choice

Find the vertex, focus, and directrix of the parabola. $( x + 5 ) ^ { 2 } = 4 \left( y - \frac { 5 } { 2 } \right)$

• A)Vertex: \(\left( - 5 , \frac { 5 } { 2 } \right)\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• B)Vertex: \(\left( \frac { 5 } { 2 } , - 5 \right)\) ; Focus: \(\left( - 5 , \frac { 3 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• C)Vertex: \(\left( \frac { 5 } { 2 } , - 5 \right)\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 3 } { 2 }\)
• D)Vertex: \(\left( - 5 , \frac { 5 } { 2 } \right)\) ; Focus: \(\left( - 5 , \frac { 3 } { 2 } \right)\) ; Directrix: \(y = \frac { 7 } { 2 }\)
• E)Vertex: \(( 0,0 )\) ; Focus: \(\left( - 5 , \frac { 7 } { 2 } \right)\) ; Directrix: \(y = \frac { 7 } { 2 }\)

---

Definitions:

Adjustment Difficulties

Challenges or problems in adapting to new situations, environments, or changes in one's life.

Health Problems

Any issues or conditions, whether physical or mental, that affect an individual's overall well-being and functioning.

Intense Distress

A state of extreme anxiety, sorrow, or pain that overwhelms an individual's ability to cope effectively.

Kübler-Ross's Theory

A theory outlining five stages of grief that individuals go through: denial, anger, bargaining, depression, and acceptance.