Quadratic Expressions
Completing the Square
Exercise 1
Complete the square on each of the following.
(a) x
- 6x + 5
(b) 2z + 8z + 9
(c) 2w - 5w + 7
(d) 3y + 2y + 2
Solution
(a) Here x - 6x + 5 = [x - 6x] + 5
= [x - 6x + (3) - (3)] + 5
= [(x - 3) - 9] + 5
= (x - 3) - 4
(b) 2z + 8z + 9 = 2[z + 4z] + 9
= 2[z + 4z + (2) - (2)] + 9
= 2[(z + 2) - 4] + 9
= 2(z + 2) + 1
(c)
(d)
Quiz
Which of the expressions below is obtained after completing
the square on 2x - 3x + 5?
Solution
We have 2x - 3x + 5 = x 3
