Accelerated Algebra 2
Final Formulas
Equations of Lines
Slope = m =
y 2  y1
x 2  x1
Slope-intercept:
y = mx + b ;
Point-slope:
y – y1 = m(x – x1) ;
Standard Form:
Ax + By = C ;
A
m= 
B
m = slope, b = y-intercept;
given point (x1, y1), m = slope
A, B, & C are integers, do not lead equation w/a negative #
x-intercept =
C
A
y-intercept =
C
B
(x, y) is a solution to each type of equation (is a point on the line)
parallel lines have same slope
perpendicular lines have opposite reciprocal slopes
For x-intercept set y = 0 and for y-intercept set x = 0.
Rules of Radicals
1
an 
and
a
a 
m n
n
a
mn
ab  a  b
n
n
1
a n
ab
m
am an  amn
 an
n
n
a a
   n
b b
a b
m m
n
a

b
n
n
am
 amn
n
a
a  bm  a  b.....m times
a
b
Solving by Factoring/Foiling
#1 Rule: Always take out the GCF and write in descending order
Two Terms: Difference of 2 Squares
Sum of 2 Cubes
Difference of 2 Cubes
Three Terms:
(a)2 – (b)2 = (a – b)(a + b)
(a)3 + (b)3 = (a + b)(a2 – ab + b2)
(a)3 – (b)3 = (a – b)(a2 + ab + b2)
(a + b)2 = a2 + 2ab + b2
(a – b)2 = a2 – 2ab + b2
F & S table then grouping - factors of 1st and 3rd term that add to 2nd term
Perfect Squares
Accelerated Algebra 2
Final Formulas
4x3 + 10x2 – 6x → 2x(2x2 + 5x – 3) →
Short cut:
2x 2
2x 2
,
x
6x
2x
x
,
1 3
2x(2x – 1)(x + 3)
Four Terms:
Grouping method
If cannot factor, Complete the Square or Quadratic Formula
Completing the square:
0 = 2x2 + 4x – 8 ,
8 + 2 = 2(x2 + 2x + 1) , 10 = 2(x + 1)2
5 = (x + 1)2
 5 =x+1
–1  5 = x
Quadratic Formula:
x=
 b  b 2  4ac
2a
Discriminant: b2 – 4ac
>0 two real roots, = 0 1 real root, <0 2 imaginary roots
(nature of the roots, # of x-intercepts)
Writing Equations of Quadratics
Sum and Product of the roots:
Conic Sections
0 = ax2 – (sum)x + product
a, b, c must be integers
s1+s2 = sum
s1·s2 = product
a=1
Vertex: x or y =
b
2a
y = ax2 + bx + c / y = a(x – h)2 + k
x = ay2 + by + c / x = a(y – k)2 + h
(x – h)2 + (y – k)2 = r2
Parabola - 1 squared term
Circle – 2 squared terms same coefficient
Ellipse – 2 squared terms, different positive coefficients
Hyperbola – 2 squared terms, 1 positive, 1 negative
x  h 2   y  k 2 1
a 2 or b 2
 x  h 2
a 2 or b 2
Distance/Midpoint Formulas
d=
x2  x1 2   y2  y1 2
Midpoint (xm,ym)
xm =
x1  x2
2
ym =
y1  y 2
2
a 2 or b 2

 y  k 2  1
a 2 or b 2
V(h, k)
V(h, k)
C(h, k)
V(h, k)
V(h, k)
Accelerated Algebra 2
Final Formulas
Logarithms
log b a = n
→ bn = a
a > 0, b > 0, b ≠ 1
log b a = log b c then a = c
log b a + log b c = log b ac
log b a – log b c = log b
a
c
nlog b a = log b an
log b 1 = 0
log b b = 1
log b a =
b
log b a
log
c
a
log c b
a
ln x = log e x
a)
b)
c)
ln 1 = 0
ln e = 1
e ln a = a
Sequences
Arithmetic sequence: tn = t1 +(n – 1)d
d = common difference
Geometric sequence: t n  t1  r n 1
r = common ratio
Permutations
Arrangements; order matters
n
Pr 
n!
(n  r )!
Combinations
Order does NOT matter (thinks groups)
n
Cr 
n!
r!(n  r )!
Accelerated Algebra 2
Final Formulas
Direct Variation:
y  kx
*k is the constant of variation
Solve for k first and then answer question
Inverse Variation:
y
k
*k is the constant of variation
x
How to find zeros of a function:
Set the equation equal to zero and solve!
How to find domain of a function:
Think x, check the restrictions of the function
f ( x) 
x4
Domain: all reals except -2
x2