Quadratic Expressions Worksheets Page 20
ADVERTISEMENT
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36number and algebra
7.5 Factorising by completing the square
Completing the square
Completing the square
•
is the process of writing a general quadratic expression in
int-2783
int-2783
int-2783
turning point form.
Complete the square
+ bx + c = a(x − h)
+ k
2
2
ax
General form
Turning point form
2
+ 8x can be modelled as a square with a smaller square missing from
• The expression x
the corner, as shown below.
8
x
+ 4
x
+
=
8x
x
2
x
x
2
4x
x
x
x
+
4
4x
x
4
+ 8x
=
(x + 4)
– (4)
x
2
2
2
4
half of the coeffi cient of x; that is, the area of the small square is a
b
• In ‘completing the square’, the general equation is written as the area of the large square
minus the area of the small square.
2
+ bx, the small square has a side length equal to
• In general, to complete the square for x
2
b
.
2
b
+
x
b
x
2
b
+
=
2
x
2
x
x
x
x
x
x
bx
2
+
b
b
x
2
2
x
b
2
b
(
)
) (
b
2
b
2
+ bx
=
2
x +
–
x
2
2
2
287
Topic 7 • Quadratic expressions
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education