Ch. 9 Test Review (9.1-9.5) Math 102
Chapter 9 is about solving quadratic equations. A quadratic equation is an equation for which
the highest power of the variable is 2, and any quadratic equation can be written in the form:
2
0
ax bx c
+ + =
We learned how to solve these equations by factoring in ch. 6, but not all quadratic equations
can be solved with this technique. In ch. 9, we learn to solve by two new methods: completing
the square and the quadratic formula. New types of solutions are discovered – some of which
aren’t even “real” numbers! Note that there are always 2 solutions to a quadratic equation.
9.1: This section was preparation for completing the square in section 9.2. The main idea is
that if you have an expression of the form:
( )
2
variable expression constant
=
then you can write down two solutions:
variable expression = + constant
and
variable expression = - constant
Symbolically, the rule was summarized as:
If 2
x a
=
, then
x a
= ± .
You should note that the equation may have to be modified to fit this form before you
“take the square root of both sides”. The left hand side must be only the square of a
variable expression!
Note that if a quadratic equation is presented to you in this format, taking the square root
of both sides is by far the most convenient solution method.
9.2: Completing the square
The point of completing the square is to force any quadratic equation into the format in
9.1 above. This is done by simple algebra tricks, but the process can still be very
confusing:
1. Get all variables on one side, constants on the other.
2. Get a coefficient of 1 on the quadratic term.
3. Guess the binomial you square to get all the same variable parts.
4. Compensate for the constant you’ve implicitly added to the variable side.
