6
AssignmentMultiple Choice

Conic Sections: Parabolas

Question 6 • TX-Pre-Calculus

Write the equation for a parabola with the vertex at (–1, 3) and the equation of the directrix y = 1.

Answer
A
(x – 1)2 = (y + 3)
B
(x + 1)2 = 8(y – 3)
C
(x – 1)2 = 8(y + 3)
D
(y – 3)2 = 2(x + 1)

Explanation

For a vertical parabola, the standard form is (x − h)² = 4p(y − k), where (h, k) is the vertex. The directrix is 2 units below the vertex, so p = 2 and the parabola opens upward. Substituting h = −1, k = 3, and p = 2 gives (x + 1)² = 8(y − 3), which is choice B.

AI-written and checked against the verified answer.

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