5
AssignmentMultiple Select

Conic Sections: Parabolas

Question 5 • TX-Pre-Calculus

Which of the following statements are true about the graph of (y + 5)2 = 10(x – 2)? Check all of the boxes that apply.

Answer
A
The graph opens to the right.
B
The vertex is at (–5, 2).
C
p = 2.5.
D
The focus is found using the formula (h, k + p).
E
The directrix is at x = –2.5.
F
The axis of symmetry is at y = –5.

Explanation

Compare the equation with the standard form (y − k)² = 4p(x − h). Here h = 2, k = −5, and 4p = 10, so p = 2.5. Since p is positive, the graph opens to the right, and its axis of symmetry is y = −5. The vertex is (2, −5), not (−5, 2); the focus formula is (h + p, k), and the directrix is x = h − p = −0.5.

AI-written and checked against the verified answer.

Previous
Next