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Name:_____________________________________________ Date:________ Period:______ Regents & Final Study Guide Algebra 2 Regents & Final Study Guide Important Information to Remember: Equations: Quadratic Formula: Discriminant: “nature of the roots” formula: b2 – 4ac b2 – 4ac < 0 : imaginary roots b2 – 4ac = 0 : real, rational, and equal roots b2 – 4ac > 0 & a perfect square: real, rational, and unequal b2 – 4ac > 0 & a non-perfect square: real, irrational, and unequal Sum of the roots: Product of the roots: Axis of Symmetry: How to find a quadratic equation using sum & product of roots: x2 – (sum)x + (product) = 0 Equation of a circle (center-radius form): (x – h)2 + (y – k)2 = r2 where (h,k) = center and r = radius If you are given an equation of a circle in standard form and need to write it in center-radius form, you must perform completing the square twice. Remember to group the x’s and y’s together. Rational Expressions: Simplifying a Complex Fraction: find an LCD, then multiple each “little” fraction by the LCD. Once that is completed, factor both the numerator & denominator then reduce. Rational Equations: To solve these, you must find an LCD. Multiply each fraction by the LCD to reduce out the denominator. Then solve like a regular equation. You must check your answer to make sure that the fraction is not undefined. Adding & Subtracting Rational Expressions: To simplify , first factor the denominators, then find an LCD. Once you find an LCD, multiply each fraction by what is “missing”. Then, combine like terms across the numerator, leaving the denominator as the LCD. All answers must be in simplest form. Multiplying Rational Expressions: Factor every numerator and denominator. Simplify the expression by reducing any numerator with any denominator. Rewrite as one fraction. Dividing Rational Expressions: Change a division problem into a multiplication one by multiplying by the reciprocal. Then complete the problem as you would a multiplication one. Radicals: Fractional Exponents: or To Solve Radical Equations: Isolate the radical. Then square both sides. Make sure you check your answers. Simplifying Radicals: Look for perfect powers. For example, if you are taking a square root, look for perfect squares. Functions: Domain: set of all of the x-values Range: set of all the y-values One-to-One: none of the elements in the range is used more than once. Onto: all the elements in the range are used. Vertical Line Test: used to tell if a graph is a function. If a vertical line intersects the graph more than once, then it is not a function. Horizontal Line Test: used to tell if a graph of a function is one-to-one. If a horizontal line intersects the graph more than once, then it is not a one-to-one function. Trig Functions: Soh – Cah – Toa Cofunctions: x + y = 90 Radians Degrees: Arc Measure: arcsin x = sin-1x Degrees Radians: , where s = arc length, arccosx = cos-1x = angle, in radians, and r = radius arctanx = tan-1x Reference Angles: You are looking for the reference angle. Trig Equations: For all trig equations you must find the reference angle and quadrants that the angle terminates in. Then, use the reference angle to find your answer. QI: Angles in QI are their own RA QII: 180 – RA QIII: 180 + RA QIV: 360 - RA Trig Identities: Trig Graphs: y = asinbx y = acosbx |a| = amplitude |b| = frequency frequency: how many complete cycles you see from 0o – 360o period: how long it takes to complete 1 full cycle y = a sin (b(x – c)) + d y = a cos (b(x – c)) + d c: horizontal shift d: vertical shift Exponential Functions & Logs: The inverse of an exponential function is a log. The inverse of a log is an exponential function. is equal to Log Rules: (1) (2) (3) Probability & Statistics: Bernoulli’s Theorem: nCr sr fn-r where n = # of trials, r = “exactly” # times, s = probability of success, f = probability of failure s + f = 1 (therefore s and f must be written as either a fraction or a decimal) at least # of trials: you must find the probability of that number and everything greater than it, until you reach the total number of trials. at most # of trials: you must find the probability of that number and everything less than it, until you reach the exact probability of 0. Binomial Expansion: find the rth term: nCr – 1 an – (r – 1) br – 1