Standard Form (Linear)
Difference of Squares
General Form (Quadratic)
(x
ax 2 + bx + c = 0 or
Point-Slope Formula
y − y1 = m(x − x1 )
Sum of Squares
Standard (Vertex) Form
x 2 + y 2 ; prime
Perfect Square Trinomial
y = mx + b
Quadratic Formula
Slope Formula
− b ± b 2 − 4ac
x=
2a
y 2 − y1
x 2 − x1
r=
⎛ x 2 + x1 y 2 + y1 ⎞
,
⎜
⎟
2 ⎠
⎝ 2
n
0
.
n
(
n
x = x
x
)
z
=
1
(x )
= x zn
(xy )z
= xz yz
z n
n
n
n ≠ 0
;
x
z
= x
Sum of Cubes
( x − h )2 + ( y − k ) 2
z
n
(
x3 + y 3 = ( x + y ) x 2 − xy + y 2
x z xn = x z +n
xn + xn = 2xn
x
=
y
2xn − xn = xn
b
b log b
log a y
log b y =
log a b
EAP/GWL
)
▲ Tip: Use S.O.A.P. to remember
the signs in the Diff. and Sum of
Cubes formulas—Same, Opposite,
Always Positive.
log
log
)
xn
n− z
=
x
;
z
x
x≠0
1
0
(
x 3 − y 3 = ( x − y ) x 2 + xy + y 2
(h,k) is center of circle
⎛ xz ⎞
x zn
⎜⎜ z ⎟⎟ = zn ;
y
⎝y ⎠
y≠0
2
Difference of Cubes
⎛ −b
⎛ − b ⎛ − b ⎞⎞
b ⎞
(h, k ) = ⎜⎜
, f⎜
, c − ⎟⎟
⎟ ⎟⎟, or ⎜⎜
2
a
2
a
2
a
4
a⎠
⎝
⎠⎠
⎝
⎝
Equation of a Circle
Midpoint Formula
2
x 2 − 2 xy + y 2 = (x − y )
2
(x 2 − x1 )2 + ( y 2 − y1 )2
1
x 2 + 2 xy + y 2 = ( x + y )
Vertex of a Parabola
Distance Formula
d=
)
− y 2 = (x − y )( x + y )
f ( x ) = ax 2 + bx + c; f ( x) = y
Slope-Intercept Form
m=
2
log 1
0; log 0
log
.
log b M
b =1
x
p
= x
= P log b M
log b x = log b y ⎯
⎯→ x = y
◄Tip: Use the change of base formula log
to convert to base 10 (log) or e (ln),
which can be solved using a calculator. log
1/2011
x
; y ≠ 0
y
b
b
MN = log
M
= log
N
b
b
M + log
b
N
M − lob b N
LSC-O