warm-up 1.what are the different ways to solve quadratic equation? solve the following problem by...
TRANSCRIPT
Warm-up
1. What are the different ways to solve quadratic equation?
Solve the following problem by completing the square.
22. 10 16x x
Objective - To solve quadratic equations by completing the square.
Methods for Solving Quadratic Equations1) Square Root Method (Doesn’t work with
linear terms)
x2 92) Graphic Method
y x2 2x 3(Often difficult to tell)
x=-1 x=3
3) Quadratic Formula
0 x2 2x 3a=1b= -2c= -3
x b b2 4ac
2a
(Always works)
4) Factoring Method
0 (x 1)(x 3)(Works when factorable)
5) Completing the Square (Always works)
2
Solve by completing the square.
x2 5x 6 0
6 6
x2 5x 6
Complete the square
254
52
254
254
x2 5x 254
244
254
x 52
2
14
x 52
1
4
x 52
12
x 52
12
52
12
52
12
3
,2
#1
2
Solve by completing the square.
x2 7x 0
x2 7x 0
Complete the square
494
72
494
494
x2 7x 494
494
x 72
2
494
x 72
49
4
x 72
72
x 72
72
72
72
72
72
7
,0
#2
2
x2 72
x 2
Solve by completing the square.
2x2 7x 4 0
4 4
4916
12
72
4916
4916
x 74
2
8116
x 74
81
16
x 74
94
x 74
94
74
94
74
94
2x2 7x 4
2 2
x 74
2
3216
4916
74
2
74
74
24
164
12
, 4
#3
2
x2 53
x 13
Solve by completing the square.
3x2 5x 1 0
1 1
2536
12
53
2536
2536
x 56
2
1336
x 56
13
36
x 56
136
x 56
136
3x2 5x 1
3 3
x 56
2
1236
2536
56
2
56
56
x 5 13
6
#4
Practice21. 3 0x x
Practice22. 3 6 2 0x x
Practice23. 3 4 1 0x x
Practice24. 4 4 11 0x x
Complete the square using your white board.26 24 41 0x x