Derivation Of The Quadratic Formula Worksheet With Answer Key Page 3
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5Algebra 1
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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
Directions
Algebraic Representations
Divide the general form of a quadratic
€
equation by a.
Step 1:
c
Subtract the constant
from both sides of
Step 2:
a
the equation.
Take half of the coefficient of the linear term,
square it, and add it to both sides of the
Step 3:
€
equation.
Factor the trinomial on the left side of the
equation.
Step 4:
2
b
"
$
Multiply out
on the right side of the
Step 5:
#
%
2a
equation.
c
Multiply
by an equivalent form of one to
−
Step 6:
a
€
obtain common denominators.
Combine the fractions on the right side of the
equation.
Step 7:
€
Take the square root of both sides of the
equation.
Step 8:
2
b
"
$
Simplify
on the left side of the
x +
Step 9:
#
%
2a
equation.
a
a
Use the property
on the right side
=
Step 10:
b
b
€
of the equation.
2
Simplify
on the right side of the
4a
Step 11:
equation.
€
b
Subtract
from both sides of the equation.
€
Step 12:
2a
Combine the fractions to obtain the Quadratic
Formula.
Step 13:
€
MCC@WCCUSD 12/02/11
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