Cassie GrecoAlgebra 2 & Trig ReviewAFTER THEY CLEAR YOUR CALCULATOR YOU MUST PERFORM THESE STEPS!!!!!!*****THEY WILL NOT TELL YOU HOW TO DO THIS*****MODE A+BIMODE DEGREE2ND CATALOG (SCROLL DOWN TO) DIAGNOSTIC ON Undefined FractionsA fraction is undefined when its denominator equals zero. Here you set the bottom equal to zero, then solve for x. Simplifying FractionsTo simplify a fraction containing variable expressions factor first. Adding and Subtracting ExpressionsWe can only add and subtract fractions with the same denominator. If the denominators are different you must find the least common denominator. Dividing FractionsMultiply dividend by reciprocal of divisor. ** KEEP-CHANGE-FLIP RULE!!!! KEEP the first fraction CHANGE to multiplication FLIP the second fraction*** Complex Rational ExpressionsFractions whose numerator, denominator, or both contain fractions. To simplify a complex fraction first find the LCD of all the little fractions. Second multiply every term by the LCD. Third factor and reduce. Solving Rational ExpressionsThis contains one or more fractions. To solve: first find the LCD of all the fractions. Second, multiply every term by the LCD to remove fractions. Third, solve. Fourth, check. Fifth, reject any extraneous roots (any solution for which the equation is undefined is called an extraneous root.) Absolute Value Equations When solving an equation containing absolute value you must first isolate the absolute value then set up the cases. EX: original l2x-4l =8 two cases are 2x-4=8 and 2x-4=-8. Absolute Value InequalitiesTo solve an inequality containing absolute vale the inequality must first be converted to either a conjunction or a disjunction. EX: -any numberany number. < and mean and. Therefore you shade in on number line. > and mean or. Therefore you shade out on number line. When making the second case negative change the sign. When dividing by a negative change the sign. Roots and RadicalsEvery positive real number has two square roots positive and opposite. You will never have a negative inside the radical. Inside of the radical must always be greater than or equal to zero. Simplifying RadicalsA radical is in simplest form if the radicand does not contain any perfect square factors. The radicand does not contain a fraction. The radical does not appear I a denominator of a fraction. When there is an exponent you can simplify those too by dividing exponent by the index number. Adding and Subtracting RadicalsRadicals that have the same index and same radicand are called like radicals. Like radicals can be added or subtracted. You can subtract/add the outside and keep the inside as long as they are the same. Multiplying RadicalsRadicals can be multiplied when the indexes are the same. First you multiply coefficients and multiply radicands. Then simplify. Dividing RadicalsRadicals can be divided when the indexes are the same. Divide coefficients, divide radicands. Then simplify. Rationalizing a DenominatorThis means to write the fraction as equivalent fraction with a denominator that is a rational number. (Just multiply top and bottom by the denominator) Binomial DenominatorsTo rationalize a fraction whose denominator is a binomial, multiply numerator and denominator by conjugate of denominator. ********** CONGUGATE JUST CHANGE THE SIGN********** a+bi is a-bi. Solving Radical EquationsContain one radical term with a variable in the radicand. Isolate radical on one side, square both, solve, then check. Introduction to Complex Numbersi imaginary unit not real. i = radical -1. Always remove the negative inside a square root and put i in the front before doing any calculations. Powers of i Put in calculator. Calculator Steps: MathNUM #3 (iPart) 2nd period (i) raise it to whatever power you are looking for. Additive InverseChange both signs. a+bi is a-bi

Adding Complex NumbersCombine like terms. (3+4i) + (5+6i)= 8+10i Subtracting Complex NumbersDistribute and combine like terms. (4+3i) (5+2i)= 4+3i-5-2i= -1+i Multiplying Complex NumbersUse foil. Division of Complex NumbersTo rationalize a fraction whose denominator is in the form a+bi we must multiply the denominator and numerator by its conjugate. Solving Quadratic EquationsWrite in standard form (set = to 0). Factor. Set each to 0. Solve both. Check in equation. Quadratic InequalitiesContains a polynomial of degree 2. EX: ax2+bx+c and shade out on number line. If it is equal to you fill in the circle. Then write the appropriate solution. Completing the SquareCoefficient of the highest power =1. Move constant term to the right. Prepare to add needed value to create a trinomial. To find value, take half the coefficient of middle term, square it, and add value to both sides. Factor. Take square roots. solve. Quadratic FormulaEquation in the song to the beat of pop goes the weasel:X equals negative b plus or minus the square root. B squared minus four ac all over two a.

DiscriminantThis is the name given to the expression that appears under the square root (radical) sign in the quadratic formula. The discriminant of the quadratic equation is: the discriminant tells you about the nature of the roots.

Value of the DiscriminantNature of the Roots

POSITIVE b^2-4ac > 0Positive and Perfect Square: Real Rational, Unequal.Positive, and Not a Perfect Square: Real. Irrational, Unequal

ZERO b^2-4ac=0Real, Rational, Equal

NEGATIVE b^2-4ac0. Equation of a Circle

(h,k) is the center and r is the radius. Steps to Find Center and Radius of an EquationFirst, move the constant to the other side. Second, group x and y terms together. Third complete the square for each set. Fourth , factor out each set of the parenthesis. Now the equation is in center radius form. Solving higher degree polynomialsA polynomial function of degree two has one turning point and at most two real roots or zeros. A polynomial function of degree three has at most two turning point. It can have one or three real roots, or zeros. A polynomial function of degree n has at most n distinct roots. to find the degree look at highest exponent. All you do is factor. Inverse variationTwo things being compared will change in opposite directions. As one increases the other decreases. X and y vary inversely or are inversely proportional when xy=xy. When the ration of two variables is a constant, the variables are directly proportional. Set up a proportion.

Laws of Exponents

Zero exponentAnything to the 0 power equals 1. Negative ExponentAnything that has a negative exponent put 1 over that number raised to that number. X^-n = 1/x^n Solving Equations Involving ExponentsGet variable with exponent alone. Raise both sides to reciprocal of given exponent. Simplify and check. Solving Exponential ExponentsExpress each side as a power of the same base. Set exponents equal to each other. Solve. Exponential Functions and Their GraphsFunction of form y=b^x. b= a positive number not equal to 1. b>1=function increases. 0