-1, 10

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 13T
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Question
A graphing calculator is recommended.
This exercise deals with confocal parabolas, that is, families of parabolas that have the same focus.
(a) Draw graphs of the family of parabolas
= 4p(y + p)
3
-1,
2
3
1,
2
1
1
for p = -2,
2.
2
10
Graph Layers
«
Clear All
9
After you add an object to the graph you
8
Delete
can use Graph Layers to view and edit its
properties.
5
Fill
3
2
1
-10 -9
-8
-7 -6
-5
-3
-2 -1
1
3
4
6
8
9
10
-1
-2
No
Solution
-3
-4
-5
-6
-7
-8
-9
-10
Help
WebAssign. Graphing Tool
(b) Show that each parabola in this family has its focus at the origin.
The graph of x² = 4p(y + p) is obtained by shifting the graph of x2
= 4py vertically
units so that the vertex is at (x, y) = (
). The focus of x2 = 4py is at (x, y) = (
), so this point is also shifted
units vertically to the point (x, y) = (
). Thus, the focus is located at the origin.
(c) Describe the effect on the graph of moving the vertex closer to the origin.
The parabolas become ---Select--- v as the vertex moves toward the origin.
Submit Answer
Transcribed Image Text:A graphing calculator is recommended. This exercise deals with confocal parabolas, that is, families of parabolas that have the same focus. (a) Draw graphs of the family of parabolas = 4p(y + p) 3 -1, 2 3 1, 2 1 1 for p = -2, 2. 2 10 Graph Layers « Clear All 9 After you add an object to the graph you 8 Delete can use Graph Layers to view and edit its properties. 5 Fill 3 2 1 -10 -9 -8 -7 -6 -5 -3 -2 -1 1 3 4 6 8 9 10 -1 -2 No Solution -3 -4 -5 -6 -7 -8 -9 -10 Help WebAssign. Graphing Tool (b) Show that each parabola in this family has its focus at the origin. The graph of x² = 4p(y + p) is obtained by shifting the graph of x2 = 4py vertically units so that the vertex is at (x, y) = ( ). The focus of x2 = 4py is at (x, y) = ( ), so this point is also shifted units vertically to the point (x, y) = ( ). Thus, the focus is located at the origin. (c) Describe the effect on the graph of moving the vertex closer to the origin. The parabolas become ---Select--- v as the vertex moves toward the origin. Submit Answer
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