Completing the Square:
Answers to Odd Numbered Problems
Fall 2009
1a. x2 + 16x = (x
+ 8)2 – 64
3a. x2 + 4x + 5 = (x
+ 2)2 + 1
5a. x2 – 8x + 11 = (x
– 4)2 – 5
Graphs are required
for (b), but will not be reproduced here.
Your graphs should reflect the following information:
|
Problem |
Vertex |
x-Intercept(s) |
y-Intercept |
|
1b |
(–8, –64) |
(–16, 0) and (0,
0) |
(0, 0) |
|
3b |
(–2, 1) |
none |
(0, 5) |
|
5b |
(4, –5) |
hard to graph
exactly |
(0, 11) |
|
7b |
(7/2, –49/4) |
(0, 0) and (7, 0) |
(0, 0) |
|
9b |
(5/2, 7/4) |
hard to graph
exactly |
(0, 8) |
11. 10t2 – 60t = 10(t – 3)2 – 90
13. 3y2 + 18y
– 20 = 3(y + 3)2 – 47
19. –5p2 + 10p – 70 = –5(p – 1)2 – 65
Revised Friday, May 1, 2009. E-mail corrections, suggestions to mmaltenfort@ccc.edu