Grade 11 - More Exercises.
Completing the square.
Write the following expressions in the form (x + p) 2 + q by completing the square and then write down the maximum or minimum value of the expression :
1.
x 2 + 2x + 3
2.
x 2 - 3x - 2
3.
x 2 + 4x - 3
4.
x 2 - 5x + 6
5.
a 2 - 3a + 1
6.
2a 2 - 3a + 8
7.
3p 2 - 4p - 2
8.
8q 2 + 3q - 5
9.
7x 2 - 2x - 5
10.
-x 2 - 2x + 3
11.
−y 2 + 5y - 6
12.
-x 2 + 3x + 1
13.
−y 2 - 5y - 8
14.
−3a 2 - 2a - 1
15.
-2a 2 - 3a + 2
16.
−4p 2 + p - 1
17.
−3q 2 + 2q - 8
18.
-5x 2 - 3x - 7
B.
What must be added to each expression so that the sum is a complete square?
19.
x 2 + 2x
20.
y 2 - y
21.
a 2 + 2a + 4
21.
a 2 + 2a + 4
22.
p 2 + 2p - 3
23.
q 2 - 3q - 5
24.
a 2 + 2a - 5
25.
2p 2 + p - 1
26.
3q 2 + 2q + 4
27.
5x 2 - 3x + 2
28.
6x 2 - 5x + 9
29.
7y 2 + 5y + 4
30.
8z 2 - 3z - 7