P
ERFECT
T
RINOMIALS
:
When a perfect trinomial is factored, both binomials will be equal
The third term in a perfect trinomial is equal to the second
term divided by 2 and then squared
The term in the binomial is equal to the second term divided
by 2
When we CTS, we change the trinomial into a perfect
trinomial
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W
HAT
IS
“C
OMPLETING
THE
S
QUARE
”
“Completing the Square” is a process that converts a
quadratic function that can not be factored to a form that
can be solved algebraically
Suppose we have the following trinomial
If we complete the square, we end up with the expression
on the right
Can’t factor this…
We end up with two answers
in radical form
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H
OW
TO
C
OMPLETE
THE
S
QUARE
Bracket the first two terms!
Divide the second term by 2 and
square it!
Purpose: Make the expression in the
bracket into a perfect square!
Take the negative square outside
of the brackets!
The trinomial becomes two
equal binomials
Now you can solve this equation by
square rooting both sides:
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E
X
: C
OMPLETE
THE
S
QUARE
AND
S
OLVE
FOR
“
X
”
Bracket the first two terms!
Divide the second term by 2 and
square it!
Take the negative square
outside of the brackets and
multiply with coefficient in
front!
The trinomial becomes two
equal binomials
Solve for “x” by square
rooting both sides
Factor out any coefficient for x
2
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Ex: The sum of two numbers is 80. Their product is
1600. Find the numbers
Gather
Information
There are two numbers, let ‘x’ and ‘y’
be the numbers
The sum is 80
The product is 1600
Substitute the first equation
into the second one.
The two numbers
are 30 and 80
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Ex: The difference of two numbers is 10. The sum of
their squares is 60. Find the numbers
Gather Information
There are two numbers, let ‘x’ and ‘y’
be the numbers
The difference is 10
The sum of their
squares is 60
Substitute the first equation
into the second one.
The two sets of numbers
are:
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Find the vertex because:
The vertex is the minimum
1. Complete the square
The minimum
occurs when x =-5
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H
OMEWORK
:
How to Complete the square assignment
-
/ 9
Menu
Slides
Notes
1. How to Complete the Square
2. Perfect Trinomials:
3. What is “Completing the Square”
4. How to Complete the Square
5. Ex: Complete the Square and Solve for “x”
6.
7.
8.
9. Homework:
H
OW
TO
C
OMPLETE
THE
S
QUARE
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