Algebra Formulas 
                    Geometry         Quadratic Equation 
                                                         2           2    2                                                2
                                                  ()()
                    Equation of a circle:          x − h   + y−k =r ,        ax +bx+c=0 
                                                              ()
                       Center = h,k , Radius = r 
                    Quadratic Function:  y = ax2 +bx+c,        Quadratic Formula 
                                                              ⎛    b         b2 ⎞                                          −b± b2 −4ac
                                                              ⎜                  ⎟
                       Vertex =                                                        x=                                                         
                                                              ⎜− 2a,  c− 4a⎟                                                        2a
                                                              ⎝                  ⎠
                                                                    2               2
                                                         ()()
                    Distance Formula:             d =     x −x        + y −y                       
                                                            2     1        2     1
                                     y −y                                                                              1
                    Slope:  m =       2     1 , Parallel lines: m = m , Perpendicular lines:  m = −                        
                                     x −x                             1      2                                 1      m
                                      2     1                    ()                                                     2
                    Point-Slope Formula:    y − y = m x− x     
                                                          1             1
                    Slope-Intercept Form:  y = mx+b,    Horizontal Line: y = b, Vertical Line: x = a  
                                                                                    (m = 0)              (m undefined) 
                    Standard Form:                Ax+By=C     
                                                  ⎛ x + x     y + y ⎞
                    Midpoint Formula:             ⎜ 1      2 ,  1     2 ⎟     
                                                  ⎝    2          2     ⎠
                     
                    Factoring          
                    Difference of Squares:                           Perfect Square Binomials:                         
                      2      2                                                       2     2             2
                                 ()()                                       (       )
                     a −b = a−b a+b                                  (1)     a +b      =a +2ab+b   
                                                                                     2     2             2
                                                                            (       )
                         (2)    a−b =a −2ab+b                                                                          
                    Difference of Cubes                                                      
                      3     3               2           2
                                 ()(                      )
                     a −b = a−b a +ab+b                              Perfect Cube Binomials 
                                                                                     3     3       2         2     3
                                                                            (       )
                    Sum of Cubes    (1)     a+b =a +3a b+3ab +b  
                      3     3               2           2                            3     3      2          2     3
                                 ()(                      )                 (       )
                     a +b = a+b a −ab+b                              (2)     a −b      =a −3a b+3ab −b  
                     
                     
                             Exponents/Radicals                                Imaginary Number                       Absolute Value 
                      m     n     m+n               0      ()
                    b ⋅b =b                       b =1,   b ≠ 0                   i =   −1                                        x    if x ≥
                                                                                                                        x     ⎧    ,           0
                                                                                   2                                       = ⎨    x if x
                                                                                 i   =−1                                      ⎩− ,    <0
                       m n      mn                     n      n  n                              2   
                    ()                            ()
                     b      =b                     ab    =a b                    3                                     a        a
                                                                                 i   =−i                                   =
                     bm              ⎛a⎞n an                                                                                                        
                         =bm−n   ⎜ ⎟ =                               i4=1     
                       n                                      n                                                       For a >
                     b                            ⎝ b ⎠     b                                                                    0,
                      −n     1                                                                                          x =a⇔x=−aorx=a
                    b     =                
                            bn                    ⎛ a ⎞−n    ⎛ b ⎞n
                                      ()
                                                                                                                        x −a                    x < a
                                                  ⎜   ⎟    =⎜ ⎟                                                                                 and  
                                 
                      1                           ⎝ b ⎠      ⎝ a ⎠
                              n                                                                                                      ()
                                                                                                                                 ⇔ −aa⇔x<−a                  x > a
                                                  n ab = n an b                                                                                or  
                              1
                     n b =bn  
                                                    a     n a
                      nm     mn                   n              ()
                    b     = b                       b = n b ,   b ≠ 0
                                                               Area & Perimeter Formulas 
                    Area (A) is the amount of square units of space an object occupies. 
                    Perimeter (P) is the distance around a figure. 
                    1.       Square:  A quadrilateral (4-sided figure)                 2. Triangle: A 3-sided figure 
                                        o 
                     with four 90 (right) angles and four equal sides. 
                                       s 
                                                                                                                                 1
                                                          A = s2       A= B⋅h   
                                                                                               s  s 
                                                                                                1                2               2
                             s                  s                                                      h 
                                         P = 4s                                                                             P = B + s  + s  
                                                                                                     (height)                         1     2
                                        
                                        
                                       s                                                              B 
                    3.       Rectangle:  A quadrilateral with four 90o (right) angles.  4.      Right Triangle: triangle with a 90o (right)  
                                 angle 
                                                                                                         C (Hypotenuse)            1
                        A = L x W                                                          A                                  A= A⋅B
                               W                                                                                                    2
                                                                                         (Leg) 
                         (width) 
                        P = 2L + 2W      P = A +B +C 
                                
                                     L (length)                                                        B (Leg) 
                                         Pythagorean Theorem 
                                                                                                                               2      2      2
                    5.       Parallelogram: A quadrilateral with equal opposite sides.                                       A + B  = C  
                      
                          A = B x h   
                                 s                      h (height) 
                          P = 2B + 2s 
                                                        
                                          B (base) 
                     
                    6.       Trapezoid: A quadrilateral with exactly one pair of parallel sides. 
                                                 B  (base) 
                                                  1
                                                                                             1
                                                                                                 ()
                           A=hB+B  and   
                             s                                  h        s                          1      2
                              1                                           2                  2
                                                             (height) 
                           P =  B + B + s + s  
                                                                                               1      2    1     2
                                           B  (base) 
                                            2
                    7.                   
                             Circle: A set of points a constant distance (radius) from a given point (center). 
                     
                                                                                                                             Radius  (r) 
                            A=πr2                                        Diameter  (d)                                       (distance from 
                                                                        (distance across the                                 center to circle) 
                           C=2πr                                        circle) 
                                                                                                                               Circumference  
                                               d                                                                               (C) 
                           d = 2r  or  r = 2                                                                                   (distance around 
                                                                                             center                            the circle)