Derivation Of The Quadratic Formula Worksheet With Answer Key

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Derivation of the Quadratic Formula
2
General form of a quadratic equation:
ax
+ bx + c = 0,
∀a,b,c ∈ℜ, a ≠ 0
Algebraic Representations
Directions
b
c
= 0 ,
a
0
2
x
x +
+
Step 1:
a
a
b
c
2
+
=
x
x
Step 2:
a
a
2
2
b
b
c
b
2
+
+
=
+
x
x
Step 3:
a
2
a
a
2
a
2
2
b
c
b
+
=
+
x
Step 4:
2
a
a
2
a
2
2
b
c
b
+
=
+
x
Step 5:
2
2
a
a
4
a
2
2
b
c
4
a
b
+
=
+
x
Step 6:
2
2
a
a
4
a
4
a
2
2
b
b
4
ac
+
=
x
Step 7:
2
2
a
4
a
2
2
b
b
4
ac
+
=
±
x
Step 8:
2
2
a
4
a
2
b
b
4
ac
+
=
±
x
Step 9:
2
2
a
4
a
2
b
b
4
ac
+
=
±
x
Step 10:
2
a
2
4
a
2
b
b
4
ac
+
=
±
x
Step 11:
2
a
2
a
2
b
b
4
ac
=
±
x
Step 12:
2
a
2
a
±
2
b
b
4
ac
=
x
Step 13:
2
a
MCC@WCCUSD 12/02/11

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