Quadratic Equations Worksheet Page 7
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816.3 The Quadratic Formula
The quadratic formula is the most commonly used tool for solving quadratic equations because
it can be used to solve ANY quadratic equation, whether or not it is factorable (hence the name
“quadratic formula”). The only condition is that the equation be in standard form (move
everything to one side with a 0 on the other), and that you simplify your result.
THE QUADRATIC FORMULA
The solutions of any quadratic equation in standard form
+
+
=
2
ax
bx
c
0
are given by
−
±
−
2
b
b
4
ac
=
x
2
a
2
where a is the coefficient of x
, b is the coefficient of x, and c is the constant.
(NOTE: EQUATION MUST BE IN STANDARD FORM)
− x
=
2
Sample Problem:
Solve for x
x
6
3
Solution:
First note that the equation must be written in standard form, so subtract 3.
−
=
2
x
6
x
3
−
−
=
2
x
6
x
3
0
=
=
6 −
=
−
Now note that
a
1
,
b
, and
c
. 3
Now we must simplify:
Use these values in the formula.
2 ±
3 (
2
) 3
=
−
±
−
2
x
b
b
4
ac
=
2
x
2
a
=
3 ±
x
2
3
−
−
±
−
−
−
2
(
) 6
(
) 6
4
1 (
)(
) 3
=
x
2
) 1 (
The two answers are then
±
+
6
36
12
=
x
≈
=
+
x
. 6
46
x
3
2
3
2
OR
≈
−
±
=
−
x
. 0
46
6
48
x
3
2
3
=
x
2
6 ±
4
3
=
x
2
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