Math1010
Formulas to Memorize
Lines/2d Coordinates:
Distance formula (to find distance between two points
d =  x 2−x 12  y 2− y 12
 x 1 , y 1 and  x 2 , y 2  )
Midpoint formula (to find midpoint between two points  x 1 , y 1  and  x 2 , y 2  )
x x
y y
midpoint = 1 2 , 1 2
2
2


Slope formula (to find slope of line between two points  x 1 , y 1  and  x 2 , y 2  )
y 2− y 1
m=
x 2−x 1
Slope-Intercept form of a line, where m = slope and (0, b) is y-intercept of the line.
y=mxb
Point-slope form of a line, given the point
y− y 1=m x−x 1 
 x 1 , y 1  and slope m.
Parallel slope—if two lines are parallel, their slope is the same.
Perpendicular slope—if two lines are perpendicular and one line has slope m, then the
−1
other line has slope
.
m
Graphing—compared to base graph y = f(x), where c > 0
1. Shifts:
h(x) = f(x) + c ==> shifts graph up by c
h(x) = f(x) – c ==> shifts graph down by c
h(x) = f(x + c) ==> shifts graph left by c
h(x) = f(x – c) ==> shifts graph right by c
2. Reflections: g(x) = -f(x) ==> vertical reflection
g(x) = f(-x) ==> horizontal reflection
Domain:
1. For
2. For
3. For
f  x
, g  x ≠0
g  x
 f  x , f  x ≥0
loga f  x  , f  x 0
Rules of Exponents:
am⋅an=am n
am
=a m−n
n
a
abm=am b m
 am n=a mn
m
a
am
= m
b
b
0
a =1 , if a≠0
1
a−m= m
a
−m
m
a
b
=
b
a

 
1
n
a =n a
m
n
n
a =  am
n an=a , if n is odd
n a n=∣a∣, if n is even
Polynomials:
Difference of Two Squares
u 2−v 2= uv u−v
Factoring/Multiplying out squares: uv 2=u 22uvv 2 and u−v 2=u 2−2uvv 2
Quadratic formula—used to solve a quadratic equation of the form
−b± b 2−4ac
x=
2a
Logarithms:
Definition--
log a x= y <==>
Properties:
1. loga  xy=log a x loga y
x
loga
=loga x−log a y
2.
y
3. log a  x m =m log a x

y
a =x
ax 2 bxc=0