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QUADRATIC EQUATION EXTRACTING SQUARE ROOT
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  1. Understandthe Cartesian coordinate system and the idea oflocating ordered pairs of numbers.
  2. Knowand use the mid-point and distance formulas to solve real worldproblems.
  3. Knowhow to graph relations in the coordinate plane.
  4. Find domainand range of a relation from a list or ordered pairs, graph or atable of values.
  5. Recognizeand evaluate basic features of a graph of a relation.
  6. Producegraphs of simple relations using tables.
  7. Findthe x and y-intercepts of the graph of an equation(algebraically and graphically)
  8. Determinethe symmetry of the graph of an equation (algebraically andgraphically)
  9. Writethe General Form Equation of a circle in Standard Form and determinethe center and radius of the circle

BasicFeatures of a Graph

  • domainand restricted values
  • range
  • x and y intercepts
  • intervalswhere a graph is constant, increasing or decreasing

LinearEquations and Inequalities

  1. Solvelinear equations algebraically and graphically.
  2. Deal withfractional coefficients in equations.
  3. Solve equationsinvolving absolute value algebraically.
  4. Solve aformula for a given variable.
  5. Solve wordproblems by setting up and solving a linear equation in onevariable.
  6. Solve linearinequalities in one variable including compound inequalitiesand inequalities involving absolute value algebraically.
  7. Represent(graph or plot) solution sets of inequalities on the number line.

QuadraticEquations

  1. Solvequadratic equations by a variety of methods.
  2. Use thediscriminant to understand when a quadratic has no, one or two realroots algebraically.
  3. Solvesimple word problems using quadratic equations
  4. Constructand use a quadratic model to solve an application problem

Methodsof Solving Quadratics

  • Byfactoring and Using Zero Factor Property when possible.
  • By extracting square roots
  • By completing the square
  • Usingthe Quadratic formula

Polynomials andPolynomial Expressions

  1. Performbasic operations with polynomials (add, subtract, multiplyincluding FOIL)
  2. Useformulas for these special products:
  3. Factorpolynomials by factoring out the Greatest Common Factor,by grouping, and by using special products formulas for trinomials
  4. Factorsimple trinomials of form a x2 + b x +c by guess-and-check or by grouping
  5. Solvesimple equations using the Zero Factor Propertywhen possible.
  6. Solvepolynomial inequalities (degree > 1)
The Specialproducts:
  • (a+ b)2
  • (a- b)2
  • (a+ b)(a - b)

SolvingNon-linear Inequalities

  • Use critical numbers todetermine test intervals for a polynomial inequality
  • Solve a polynomialinequality algebraically and graphically
  • Construct and use apolynomial inequality to solve an application problem

Rational Expressions

  1. Know how todecide the domain of a rational expressions. (Decide what values areexcluded by the denominator.)
  2. Simplify andperform basic operations involving rational expressions (addition,subtraction, multiplication, division)
  3. Find a LeastCommon Denominator and use it to add or subtract rational expressions.
  4. Solveequations with rational expressions. Recognize that some solutions maybe extraneous and check for that.
  5. Within thecontext of sections covered, apply rational expressions to simplesituations.

OtherTypes of Equations and Inequalities

  1. Solveequations involving radicals or rational exponents
  2. Solveequations involving rational fractions
  3. Solveequations involving absolute values
  4. Solve higherdegree polynomial equations by factoring
  5. Solveequations methods as appropriate.

Equationsof the Line and Linear Inequalities

Representationsof a line:
  • Standardform: A x + B y = C where A, B, and C are any realnumbers.
  • Slope-interceptform: y = m x + bwhere m is the slope of a line and b is they-intercept.
  • Point-slopeform: y - k = m (x - h)where (h,k) is any point on the line.

SpecialSlope Relationships.

  • Horizontallines (m = 0)
  • Vertical lines (m is undefined)
  • Parallellines (m1 = m2)
  • Perpendicularlines (m1 m2 = -1)

GeneralFunction Concepts

Definitionand Notation

    1. Determineif an equation or a set of ordered pairs represents a function
    2. Usefunction notation
    3. Evaluatea function
    4. Find thedomain of a function
    5. Createand apply a piecewise-defined function.
    6. Interpretinput and output of real-life functions
    7. Solve anapplication problem involving real-life functions

Graphsof functions

    1. Finddomain and range using the graph of a function
    2. VerticalLine Test
    3. Describethe increasing and decreasing behavior of a function
    4. Classifya function as even or odd
    5. Identifysix common graphs

Transformationsof Functions

    1. Sketchthe graph of a function using common graphs and transformations
    2. Writethe equation of function using common graphs and transformations

Algebra ofFunctions

    1. Find thesum, difference, product, and quotient of functions
    2. Find thecomposition of two functions and determine the domain and range
    3. Identifya function as the composition of two functions
    4. Solvereal-life problems involving combinations and composition of functions

InverseFunctions

    1. Determineif a function has an inverse function (Horizontal Line Test)
    2. Find theInverse of a function
    3. Graph afunction and its Inverse (Know that the graph of f -1 is areflection of the graph of  f across the line y = x.)

Polynomial Functions

Polynomialdivision

    1. Dividepolynomials using long division
    2. Dividepolynomials using Synthetic division
    3. Use theRemainder Theorem to evaluate a polynomial
    4. Use theFactor Theorem to factor a polynomial

Complexnumbers (if covered by your instructor)

    1. Performoperations with complex numbers and write the results in standard form
    2. Solve aquadratic equation involving complex zeros

Polynomialanalysis

RationalFunctions

  1. Find thedomain of a rational function
  2. Find thevertical and horizontal asymptotes of the graph of a rational function
  3. Sketch thegraph of a rational function
  4. Use arational function model to solve an application problem

Exponential Functions

    1. Sketch thegraph of an exponential function
    2. Investigatebasic characteristics of an exponential function (domain,range, intercepts, increasing/decreasing behavior)
    3. Writeformulas of transformed exponential functions
    4. Use anexponential model to solve an application problem (in particular,models involving the natural exponential function)
    5. Use thecompound interest formula to solve finance problems
    6. Constructand use a model for exponential growth or exponential decay

LogarithmicFunctions

    1. Propertiesof logarithms
    2. SolveLogarithmic and Exponential Equations
    3. Sketch thegraph of a logarithmic function
    4. Investigatebasic characteristics of a logarithmic function (domain, x-intercept,vertical asymptote)
    5. Writeformulas of transformed logarithmic functions
    6. Use alogarithmic model to solve an application problem (in particular,models involving the natural logarithmic function)

Systems in twovariables

  1. Solve alinear system of equations
  2. Constructand use a linear system of equations to solve an applicationproblem
  3. Solvenonlinear systems
  4. Constructand use a nonlinear system of equations to solve anapplication problem

Methodsof Solving Systems.

  • bysubstitution
  • byelimination
  • graphically