G.GPE.A.7 WORKSHEET #2
-
PATTERSON Name:
1. Square the given binomials. Write the expression in standard form, ax' +bx + c and then write the
quadratic coefficient a, the linear coefficient, b, and the constant term, c.
a)
(x-z)') (x-A(x-z)
2-
b) (x+s)'?
.=
I
d) (x+11)'?
(x-e)' (^-
rLf
1) (x - q\
z,(--tx-txt8l
xz
xz - ts x + g \
b- -1c= I
a= I u= lO c= Zt a= [ b= -lEc= 8t
(x+r\(r+rr)
e)
x2+llx+llx*\21
X2 +
a= I
c)
tSrtSx *ZSi
xL + lox+LF
*--Zx-Zx +9
^e-t{x
(x +s)(xrs)
o=
7L
22*Y\2\
.=
\Z\
(x-1)' (*-il (x-,\
$2-lx-lx*l
xl -Zx +l
a=
[= -L c= I
t
a
(,- Ju)' (x-f,.)(x-
*r-.fi-.t x _Fx r tg
x "_ ZJE x + tr{
,=
( 6=-2I-tLl s=
2. Use the patterns found in the b and c values in question #1 to determine a way to use the linear
coefficient, b, to determine the constant value, c, for all perfect squares trinomials.
/ bt-
C = I\ -\
zl
3. Janice exclaimed after completing question
positive!!" Explain why this is true.
f1, 'The constant term,
(*"\(*") = * cz
(-") C.) = +"'
c, of all perfect squares
will be
AruY NuMBTra sgvAago)
rS Aut^rgY PostztvE.
4. Determine which of the following are perfect square trinomials.
a)
x2
+2x+l
@ or
e)
x' -70x+25
@ or
il
No
x2
Yes
No
b) x2 -8x+16
cl
@or
Yes
No
xz
Ol
or @
@or
x'-4.x-4
g)
@or
Yes or
No
t
@
+lx+2
if ,'-Sr.(|)
k) xz +l4x+28
or @
@or
Yes
No
,'.rr*(])
+4x+8
f) x2 -5x+6.25
or @
I-r,r\
No
h) x2 +20x+10
Yes
l)
x2
Yes
or @
-18x-81
t
or @
tq
G.GPE.A.I WORKSHEET #2
- PATTERSON
2
5. Determine the value of the constant term, c, to create a perfect square trinomial and then write the
trinomial in factored form.
a) x2 +4x+ {
b) x2 +10x+_L {
c) x2 +l4x+ 11
tor, (x rz)z
dl *'-l2x+ !s,
Factored tor,
( x -6)2
Factored
g)
x'-s*+--cr
4
tor, (x t 5)z
e; x'-gx+ 16
Factored
*t'"rr--*L*
Factored
h) x2 +
Factored form
9x+
4
Factored
+6x+3=0
x2
+6x+f ]=-:
xz
+6x*[f:i']=-3+(3)2
al
x2
+l0x+20=0
(
(x +3)2 = 6
x r:)'=
+llx
x
d)
| lo x + ^-.
= -ZLl
+lox+ 2{
(x+s)z --
.r-IH +?S
2
x2
+24 = 0
I
Factored form
(X
"r, ---.Ut'jszf
"r, -{r-*:ft'
y'-8y-3
=0
r;3
ut- !5*
! - 83 * 16 3+ lC
( g-')t= l9
{
Ll
Factored form
y'+ly-5=0
z
t7)
\ x2 +6.5x+ to.
bl
Factored form
c) x'
Factored
x2+t or<J- = -2o
x2 rtox l Zr z -ZO+ Zf
(x+3)2 = -3+9
tor,
fl x2-2x+ t
Factored
"rrl];l+-}[
6. Complete the square for the given quadratic equations.
x2
Factored
L
=l
I
e) x2 +6x-1 I = 0
3t*13*-.
=!
xzr6xt^- = ll
x2+6x + q = ll + i
U'*tJ * i = 5+!Ll
( u * t)'-- sLl
(x +3)t = 2o
Factored
Factored form
form (r +3\"' 2o
7. Complete the square for the given guadratic equations.
+5x-l:0
x2 +5x+f
l=t
x2
x2+5x.[(r']='.[;)'
[..(;))'=t.T
(,.(:))'=+
b)
a) x2 +z*-]=o
x?+3x+-ti
iB
(**af=
12+3x+
(x+
2)
2r-+
f
31',\
Factoredror,
(x
,'-7x-3=0
t *)z= 3
xl-Tr<+
+= 3*f
(x-r)"=+-f
(x-
2o72.
Factored form
q