Math1010 Formulas to Memorize Lines/2d Coordinates: Distance formula (to find distance between two points x 1 , y 1 and x 2 , y 2 ) d = x 2−x 12 y 2− y 12 Midpoint formula (to find midpoint between two points x x y y midpoint = 1 2 , 1 2 2 2 x 1 , y 1 and Slope formula (to find slope of line between two points x 1 , y 1 and y 2− y 1 m= x 2−x 1 x2 , y2 ) x2 , y2 ) 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− x1 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: f x , g x ≠0 g x 2. For f x , f x ≥0 3. For log a f x , f x 0 1. For Rules of Exponents: am⋅a n=amn am =am−n n a abm=a m bm 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 a n = am n n a =a , if n is odd n n a =∣a∣, if n is even n Polynomials: Difference of Two Squares u 2−v 2=uv u−v Factoring/Multiplying out squares: uv 2 =u2 2uvv 2 and u−v 2=u 2−2uvv 2 Quadratic formula—used to solve a quadratic equation of the form ax 2bxc=0 −b± b2−4ac x= 2a Logarithms: Definition-- log a x= y <==> Properties: 1. log a xy =log a xlog a y x log a =log a x −log a y 2. y 3. log a x m=mlog a x a y =x