Math1010Formulas to MemorizeLines/2d Coordinates:Distance formula (to find distance between two points x1, y1and x2, y2)d =x2−x12 y2− y12Midpoint formula (to find midpoint between two points x1, y1and x2, y2)midpoint = x1x22 , y1 y22Slope formula (to find slope of line between two points x1, y1and x2, y2)m=y2− y1x2−x1Slope-Intercept form of a line, where m = slope and (0, b) is y-intercept of the line.y=mxbPoint-slope form of a line, given the point x1, y1and slope m.y− y1=m x−x1Parallel 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 other line has slope −1m.Graphing—compared to base graph y = f(x), where c > 01. Shifts: h(x) = f(x) + c ==> shifts graph up by ch(x) = f(x) – c ==> shifts graph down by ch(x) = f(x + c) ==> shifts graph left by ch(x) = f(x – c) ==> shifts graph right by c2. Reflections: g(x) = -f(x) ==> vertical reflectiong(x) = f(-x) ==> horizontal reflection Domain:1. For f xg x, g x ≠02. For f x , f x ≥03. For logaf x , f x0Rules of Exponents:am⋅an=am naman=am−nabm=ambmamn=amnabm=ambma0=1 , if a≠0a−m=1amab−m=bama1n=naamn=namnan=a , if n is oddnan=∣a∣, if n is evenPolynomials:Difference of Two Squares u2−v2=uv u−vFactoring/Multiplying out squares: uv 2=u22uvv2and u−v 2=u2−2uvv2Quadratic formula—used to solve a quadratic equation of the form ax2bxc=0x=−b±b2−4ac2aLogarithms:Definition-- logax= y<==> ay=xProperties:1.logaxy =logax logay2. logaxy=logax−logay3.logaxm=m
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