Answer:
The equation of the parabola is (x - 2)² = 16(y + 1) ⇒ D
Step-by-step explanation:
The standard form of the equation of the parabola is
(x - h)² = 4p(y - k), where
- The vertex of the parabola is (h, k)
∵ The vertex of the parabola is (2, -1)
→ By using the notes above
∴ h = 2
∴ k = -1
∵ Its focus is (2, 3)
→ By comparing it with the notes above
∴ h = 2
∴ k + p = 3
∵ k = -1
→ Substitute it in the equation above
∴ -1 + p = 3
→ Add 1 to both sides
∵ -1 + 1 + p = 3 + 1
∴ p = 4
→ Substitute the value of h, k, p in the form of the equation above
∵ (x - 2)² = 4(4)(y - -1)
→ Remember (-)(-) = (+)
∴ (x - 2)² = 16(y + 1)
∴ The equation of the parabola is (x - 2)² = 16(y + 1)
