Chapter 10
Quadratic Equations
There are 4 different ways of solving these equations shown in your text:
factoring
(shown in Chapter 4 section 8 of text),
square root method
,
completing the square
and the
quadratic formula
.
Factoring is easiest when the
a
value is 1, but we can also use
factoring by the ac method (Section 4.6) when the
a
value is greater than 1.(Factoring
doesn’t work on all quadratic equations)
The square root method is used when there is no
x
term in the equation.
Completing the square can be used on any quadratic equation but
sometimes involves working with fractions which can be messy.
The quadratic formula
can be used on any
quadratic equation as long as you have the equation in: ax
2
+ bx + c =
0 form.
For example:
x
2
+ 2x – 15 = 0
The
a
# is 1; the
b
# is 2 and the
c
# is –15 when plugged into the quadratic formula.
If you have an equation like:
2x
2
= -8x – 3 you
need to put everything on one side of the
equal sign before you take you’re a, b, c numbers into the formula
.
So you can either
make it;
0 = -2x
2
– 8x – 3 or it can be: 2x
2
+ 8x + 3 = 0.
You will get the same solutions
from the quadratic formula with either of these equations.
Quadratic Formula:
x = -b +/-
(b^2 -4ac)÷2a
Difficulties with the Quadratic Formula:
Plugging in negative
b
values
:
In the previous example we had
a
= -2,
b
= -8 and
c
= -3
Put into the formula it would look like:
-(-8)
{(-8)² - [4(-2)(-3)]}
2(-2)
*When the
b
number is negative the negative sign in front of the
b
(far left in numerator)
stays there; so we have –(-8) (which will become positive 8).
Then under the radical sign
the
b
number is squared in the formula.
Therefore we need to put parenthesis around our
negative
b
number so that the whole thing is squared:
(-8)² = 64
FORGETTING THIS SMALL ISSUE CAN MESS UP THE REST OF YOUR

CALCULATIONS, SO TAKE CAUTION AS YOU PLUG IN YOUR VALUES!!!!
Plugging in negative
a
and
c
numbers
:
Under the radical sign we have b² - 4ac.
When you plug in a negative number for the
a
and
c
you need to be careful because of the subtract sign in front of the 4.