ALGEBRA CHEAT SHEET



ALGEBRA CHEAT SHEETLINEAR EQUATIONS1)Point Slope Formulay – y1 = m ( x – x1 )use when you have one point and the slope of the lineif you have two known points, first find the slope and then apply this formulacan be used for putting ordered pairs into standard formif you solve for y, then you can put into slope-intercept form (and then into standard form if you wish)2)Slope-intercept Formulay = m x + buse when you know the slope (m) and the y-intercept (b)if the equation is already in this form, then use to find the slope and the y-interceptuse to draw a linear graph since you know one point and the slope3)Slope Formulam = y2 – y1 / x2 - x1rise over run (change in y’s divided by change in x’s)use when you need to find the slope of two pointsafter finding the slope you can pick one of the points to develop the point slope formula, etc.4)Standard FormAx + By = Ccan be derived from the point slope formula or the slope intercept formulawhen deriving from two points, it doesn’t matter which point is used, the same standard form will resultslope m = -A/By-intercept b = C/B5)Parallel and Perpendicular Linesparallel lines have the same slope, perpendicular lines have negative reciprocal slopes FACTORING – always factor firstFOIL (first, outside, inside, last)2)Factoring Trinomials -in the form of: ax2 + bx + cmultiply a and cfind two factors of the product of a and c that equal b (watch signs)rewrite the middle term (b) as the sum of these two factorsTo group (if needed): group the first two terms and the last two termstake out the GCF of each grouprewrite the answer as two grouped multiplescheck3)Perfect Square Trinomials(x + y)2 = x2 + 2xy + y2(refer to square of a sum)(x - y)2 = x2 - 2xy + y2(refer to square of a difference)these are NOT differences of squaresrequirements:first term is a perfect squarethird term is a perfect squaremiddle term is 2 or –2 times the product of the square root of the first and the square root of the last terms.4)Polynomialsonly combine LIKE TERMSwatch negative signs – distribute them appropriately5)Differences of Squaresx2 – y2 = (x – y)(x + y) = (x + y)(x – y)if the terms of the binomial have a common factor, factor out the GCF first6)Special Productssquare of a sum(x + y)2 = (x + y) (x + y) = x2 + 2xy + y2square of a difference(x - y)2 = (x - y) (x - y) = x2 - 2xy + y2difference of squares(x + y) (x - y) = (x - y) (x + y) = x2 - y2LAWS OF EXPONENTSX-a = 1/Xa(Xa) (Xb) = Xa+b(Xa)b = XabXa/Xb = Xa-bX0 = 1 (remember, anything to the zero power is ONE)EXPONENTIAL FUNCTIONSGeneral information:first factor the base so that you have like bases on each side of the equationthen compare exponents to solve for the unknown QUADRATIC FUNCTIONS & EQUATIONSGeneral information:Quadratic equations equal “0” while quadratic functions equal “y”have either 0, 1, or 2 rootsroots (the solutions) are the points where the graph crosses the x-axis. Can be found by:graphing, or factoring and setting each factor equal to zero, or by using the quadratic formulathe standard form is ax2 + bx + cresulting graph is a parabola with a minimum or a maximumthe vertex is a minimum if the “a” coefficient is positiveNote use of square roots – they are shown using the words square root.the vertex is a maximum if the “a” coefficient is negativeFormulas and use:axis of symmetry x = -b / 2ause to find the x component of the vertexthen substitute into original equation to find the y componentdefines the equation of the axis of symmetryquadratic equationx = -b +/- square root of b2 – 4ac / 2ause to find the roots to any quadratic equationwatch the signs of a, b, cresults will be undefined if the square root has a negative value under itdiscriminateb2 – 4acuse to determine if a quadratic is factorableif positive (2 solutions), if zero (one solution), if negative (no real solutions)RATIONAL EXPRESSIONS & EQUATIONSTo simplify:use prime factorization to pair up like termsidentify excluded values before canceling (those that make the denominator equal to ZERO – meaning undefined)cancel out like termsTo multiply:first factor where possible and then cancel where possible (be careful with exponents)multiple straight across (don’t leave anything out)reduce and simplifyTo divide:flip the second term and follow multiplication rulesTo add and subtract expressions:find a common denominator (LCD works best) by factoring each denominatorchange each expression into an equivalent one with the LCD by multiplying each term by a factor to produce the LCDadd or subtract and simplifySolving equations:goal is to eliminate the denominators so identify the LCD and multiply each side of the EQUATION by the LCD to clear out the denominatorssolve for the variable (solutions that are excluded values are not actual solutions)resistance: series RT = R1 + R2 parallel 1/RT = 1/R1 + 1/R2RADICAL EXPRESSIONS & EQUATIONSPythagorean Theoremc2 = a2 + b2 where a & b are legs and c is the hypotenuse (if true then the triangle is a right triangle)Radical Expressionssquare root of ab = squate root of a X square root of bsquare root of a/b = square root of a / square root of blike radicands – add or subtract the coefficients of the like radicandsunlike radicands – simplify to like radicands if possible, then add or subtract the coefficients of the like radicandsmultiply polynomials by CONJUGATE (similar to difference of perfect squares)Radical Equationsequations with variables in the radicand – isolate the radical with the variable to one side then square both sidesdistance formula – use to find distance between 2 points on the coordinate planed = square root of (x2 – x1)2 + (y2 – y1)2can be used to determine if a triangle is isosceles (2 equal sides)completing the square – used to make a quadratic expression a perfect squarefind ? of b, square the result, add this result to the original expressionbe sure to add the resulting number to BOTH sides of the EQUATION ................
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