Quadratic Equation Worksheet - Completing The Square
ADVERTISEMENT
1
2
3
4
5
6
7
8Page 1 of 2
5.5
Completing the Square
GOAL
1
S
Q
E
OLVING
UADRATIC
QUATIONS BY
What
you should learn
C
S
OMPLETING THE
QUARE
GOAL
Solve quadratic
1
equations by completing the
is a process that allows you to write an expression of the
Completing the square
square.
2
form x
+ bx as the square of a binomial. This process can be illustrated using an
area model, as shown below.
Use completing the
GOAL
2
square to write quadratic
b
b
functions in vertex form, as
x
x
2
applied in Example 7.
( )
b
2
2
x
bx
x
x
x
x
Why
you should learn it
2
To solve real-life
2
( )
( )
b
b
b
problems, such as finding
x
2
2
2
where to position a fire
hose in Ex. 91.
2
b
2
You can see that to complete the square for x
+ bx, you need to add
, the area
2
of the incomplete corner of the square in the second diagram. This diagram models
the following rule:
2
2
b
b
2
x
+ bx +
= x +
2
2
Completing the Square
E X A M P L E 1
2
Find the value of c that makes x
º 7x + c a perfect square trinomial. Then write the
expression as the square of a binomial.
S
OLUTION
2
In the expression x
º 7x + c, note that b = º7. Therefore:
2
2
b
º
7
4
9
c =
=
=
2
2
4
2
Use this value of c to write x
º 7x + c as a perfect square trinomial, and then as the
square of a binomial.
4
9
2
2
x
º 7x +
c
= x
º 7x +
Perfect square trinomial
4
2
7
2
b
Square of a binomial: x + }
}
= x º
2
2
. . . . . . . . . .
In Lesson 5.2 you learned how to solve quadratic equations by factoring. However,
2
many quadratic equations, such as x
+ 10x º 3 = 0, contain expressions that cannot
be factored. Completing the square is a method that lets you solve any quadratic
equation, as the next example illustrates.
282
Chapter 5 Quadratic Functions
ADVERTISEMENT
0 votes
Related Articles
Related forms
Related Categories
Parent category: Education