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Your Notes
Write an equation of the parabola whose vertex is at
(2, 1) and whose focus is at (5, 1).
1. Determine the form of the
equation. Sketch the parabola.
The parabola opens to the
y
and has the form
2
(y 2 k) 2
x
2 Example 3 Write an equation of a translated parabola
5 4p(x 2 h) where
p 0.
2. Identify h and k. The vertex is at
(2, 1), so h 5 and k 5 .
3. Find p. The vertex (2, 1) and focus (5, 1) both lie on
the line , so the distance between them is
⏐p⏐ 5 ⏐ ⏐ 5 , and p 5 or p 5 .
Because p 0, it follows that p 5 , so 4p 5 .
The equation is .
Checkpoint Complete the following exercises.
1. Graph (x 2 2) 2 1 (y 1 3) 2 5 9.
Identify the center and radius.
2. Graph
(x 1 3)2
}
9
(y 2 1)2
2 } 5 1.
25
3. Write an equation of the parabola whose vertex is at
(23, 21) and whose focus is at (23, 1).
250 Lesson 9.6 Algebra 2 Notetaking Guide Copyright © Holt McDougal. All rights reserved.
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