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WHEN COEFFICIENT OF x2 = 1 |
|
y = x2 + 4x + 5
y = x2 + 4x
+ 5
y = x2 + 4x + (4/2)2
+
5 - (4/2)2
y = x2 + 4x + (2)2
+
5 - (2)2
y = (x + 2)(x + 2)
+ 5 - 4
y = (x + 2)2
+ 1
y = (x + 2)2 +
1 |
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| WHEN COEFFICIENT OF x2 IS NOT = 1 |
y = 2x2 + 4x + 3
y = 2[x2 + 2x + 1.5]
y = 2[x2 + 2x
+ 1.5]
y = 2[x2 + 2x + (2/2)2
+ 1.5 - (2/2)2]
y = 2[x2 + 2x + 12
+ 1.5 - 12]
y = 2[x2 + 2x + 1
+ 1.5 - 1]
y = 2[(x + 1)(x + 1)
+ 1.5 -1]
y = 2[(x + 1)2
+ 0.5]
y = 2[(x + 1)2
+ 2[+ 0.5]
y = 2(x + 1)2
+ 1
y = 2(x + 1)2 + 1 |
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WHEN THERE ARE TWO VARIABLES
eg Equation of a circle |
x2 + 4x + y2
- 6y -12 = 0
x2 + 4x
+
y2 - 6y -12
= 0
x2 + 4x
+
y2 - 6y
= +12
x2 + 4x + (4/2)2
+ y2 - 6y + (-6/2)2
=
+12 + (4/2)2 + (-6/2)2
x2 + 4x + (2)2
+ y2
- 6y + (-3))2
=
+12 + (2)2 + (-3)2
x2 + 4x + (2)2
+ y2
- 6y + (-3))2
=
+12 + 4 + 9
(x + 2)2
+ (x - 3)2
= 25
(x + 2)2
+ (x - 3)2
= 52
(x + 2)2 + (x - 3)2 =
52 |