Quadratic Formula Worksheet With Answer Key - Tutoring And Learning Centre, George Brown College, 2014 Page 4
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4Quadratic Formula
Where does the quadratic formula come from?
The quadratic formula can be derived by completing the square and isolating x in the
2
standard form of a quadratic relation, y = ax
+ bx + c, when y = 0 (since y is equal to 0
for any x-intercept).
2
ax
+ bx + c = 0
b
a
2
Step 1: Factor out “a” from ax
+ bx
2
a(x
+
x) + c = 0
b
b
b
b
a
a
2a
2a
−(
2
2
2
Step 2: Add and subtract half of
squared inside the
a[x
+
x +(
)
)
] + c = 0
brackets.
b
b
b
b
a
2a
2a
2a
b
− a(
2
2
2
2
Step 3: Factor the perfect square trinomial, x
+
x +(
)
.
a(x +
)
)
+ c = 0
2a
Take −(
2
)
out of the brackets by multiplying by “a.”
b
b
b2
2a
2a
4a
Step 4: Simplify the − a(
− c
2
2
)
term and move to the right
a(x +
)
=
side of the equation. Move “c” to the right side of the
equation.
b
b²
c
2a
4a²
a
b²
Step 5: Move the “a” term to the right side of the
−
2
(x +
)
=
4a
equation by dividing
and “c” by “a”
b²
c
b
b² −4ac
4a²
a
2a
4a²
2
Step 6: Subtract
and
by finding a common
(x +
)
=
denominator.
= ± �
b
b² −4ac
2a
4a²
Step 7: Take the square root of both sides of the
x +
equation.
±
� b² −4ac
b
b
2a
2a
2
Step 8: Simplify square root of 4a
in the denominator on
2a
x =−
the right side of the equation. Move the
term to the
right side.
−b ± √b
− 4ac
2
x =
2a
Step 9: Since both terms on the right side of the equation
have a common denominator, add and subtract the two
terms.
Tutoring and Learning Centre, George Brown College 2014
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