1.9 CC.912.A.REI.4b graph quadratic inequalities find solutions to quadratic inequalities


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1 1 Quadratic Functions and Factoring 1.1 Graph Quadratic Functions in Standard Form 1.2 Graph Quadratic Functions in Vertex or Intercept Form 1.3 Solve by Factoring 1.4 Solve by Factoring 1.5 Solve Quadratic Equations by Finding Square Roots 1.6 Perform Operations with Complex Numbers 1.7 Complete the Square 1.8 Use the Quadratic Formula and the Discriminant 1.9 Graph and Solve Quadratic Inequalities 1.1 CC.912.F.IF.7a* 2 explain what the parent function is identify max/min if a quadratic function find the y intercept graph quadratic function using evaluated points 1.2 CC.912.F.IF.7a* estimate the vertex of quadratic function estimate the x intercept use technology to find the x intercept 1.3 CC.912.A.SSE.3a* factor an expression to find the zeros 1.4 CC.912.A.SSE.3a* factor an expression to find the zeros 1.5 CC.912.A.REI.4b solve quadratic equations by finding square roots 1.6 CC.912.N.CN.2 identify that i is a complex number identify that is 1 use commutative & associative properties to add and subtract complex numbers use commutative, associative & distributive properties to multiply complex numbers 1.7 CC.912.A.REI.4a identify a quadratic expression identify a perfect square trinomial factor a perfect square trinomial complete the square derive the quadratic formula by completing the square 1.8 CC.912.N.CN.7 determine when a quadratic equation in standard form, has complex roots by calculating the discriminant solve quadratic equations with real numbers as coefficients express the solutions of a quadratic equation as a complex number a+bi
2 1.9 CC.912.A.REI.4b graph quadratic inequalities find solutions to quadratic inequalities 2 Polynomials and Polynomial Functions 2.1 Use Properties of Exponents 2.2 Evaluate and Graph Polynomial Functions 2.3 Add, Subtract, and Multiply Polynomials 2.4 Factor and Solve Polynomial Equations 2.5 Apply the Remainder and Factor Theorems 2.6 FindRationalZeros 2.7 Apply the Fundamental Theorem of Algebra 2.8 Analyze Graphs of Polynomial Functions 2.1 CC.912.N.RN.1 apply properties of exponents to simplify algebraic expressions with rational exponents apply the definition of the nth root 2.2 CC.912.F.IF.7c* define a polynomial identify the degree of the polynomial use technology to graph a polynomial 2.3 CC.912.A.APR.1 apply the definition of an integer apply the definition of a polynomial add & subtract polynomials multiply polynomials 2.4 CC.912.A.SSE.2 look for & identify clues in the structure of expressions to rewrite in another way explain why equivalent expressions are equivalent apply models for factoring and multiplying polynomials to rewrite expressions 2.5 CC.912.A.APR.2 divide polynomials using long division & synthetic division 2.6 CC.912.A.APR.2 apply the remainder theorem to determine if a divisor is a factor of the polynomial 2.7 CC.912.N.CN.9 (+) explain the Fundamental Theorem of Algebra in my own words by using simple polynomials & their graphs 2.8 CC.912.F.IF.7c* determine the x intercept of a polynomial when looking at a graph determine the end behavior of a polynomial by looking at the degree & leading coefficient of the equation
3 3 Rational Exponents and Radical Functions 3.1 Evaluate nth Roots and Use Rational Exponents 3.2 Apply Properties of Rational Exponents 3.3 Perform Function Operations and Composition 3.4 Use Inverse Functions 3.5 Graph Square Root and Cube Root Functions 3.6 Solve Radical Equations 3.1 CC.912.N.RN.1 Apply the definition of an nth root 3.2 CC.912.N.RN.2 Apply the properties of exponents to simplify algebraic expressions with rational exponents Write radical expressions as expressions with rational exponents Write expressions with rational exponents as radical expressions 3.3 CC.912.F.BF.1* Compose two or more functions Explain a multistep real world problem in terms of function composition and write an equation to describe the composition 3.4 CC.912.F.BF.4 Write the inverse of a function by solving Write the inverse of a function in standard notation Use the composition of functions to verify the functions are inverses Decide if the function has an inverse Use the definitions of function, inverse function, and onetoone function List the values of an inverse given a table or graph 3.5 CC.912.F.IF.7b* Explain the parent function of a square root Sketch the graph of a square root function Use technology to graph a square root function Explain the parent function of a cube root Sketch the graph of a cube root function Use technology to graph a cube root function 3.6 CC.912.A.REI.2 Solve a radical equation in one variable Determine which numbers cannot be solutions of a radical equation and be able to explain why Generate examples of radical equations with extraneous solutions
4 4 Exponential and Logarithmic Functions 4.1 Graph Exponential Growth Functions 4.2 Graph Exponential Decay Functions 4.3 Use Functions Involving e 4.4 Evaluate Logarithms and Graph Logarithmic Functions 4.5 Apply Properties of Logarithms 4.6 Solve Exponential and Logarithmic Equations 4.7 Write and Apply Exponential and Power Functions 4.1 CC.912.F.IF.7e* Explain the parent function for exponential functions Determine the domain, range, and end behavior looking at a graph Classify the graph as growth Substitute values for x, and make a table to graph the function Explain how geometric transformations changes a growth graph to decay 4.2 CC.912.F.IF.7e* Explain the parent function for exponential functions Determine the domain, range, and end behavior looking at a graph Classify the graph as decay Substitute values for x, and make a table to graph the function Explain how geometric transformations changes a growth graph to decay 4.3 CC.912.F.IF.7e* Graph logarithmic function use technology to graph logarithmic functions 4.4 CC.912.F.IF.7e* evaluate logarithmic functions when substituting values for x 4.5 CC.912.F.BF.5 (1) state the inverse of an exponential function is a logarithmic function (and vice versa) estimate or solve for the values of logarithms by evaluating powers of the base explain the inverse relationship between exponents and logarithms create the inverse of an exponential equation when given its table or graph and write the inverse in logarithmic form solve problems with variables in an exponent or logarithm by applying the inverse relationship to logarithms and exponents 4.6 CC.912.F.LE.4* define exponential function and logarithmic function write an exponential equation in logarithmic form and solve explain using the properties of exponentials and logarithms why are equivalent can use powers of 2 or 10 to estimate the value of or can use the calculator to evaluate a logarithm with a base of 10 or e and
5 apply the change of base formula to evaluate the logarithm with a base of 2 using a calculator 4.7 CC.912.F.LE.2* determine if a function is linear or exponential given a sequence, graph, verbal description, or table construct a linear function from an arithmetic sequence, graph, table of values, or a description of the relationship describe the algebraic process used to construct the exponential function that passes through two given points 5 Rational Functions 5.1 Model Inverse and Joint Variation 5.2 Graph Simple Rational Functions 5.3 Graph General Rational Functions 5.4 Multiply and Divide Rational Expressions 5.5 Add and Subtract Rational Expressions 5.6 Solve Rational Equations 5.7 Describe and Compare Function Characteristics 5.1 CC.912.A.CED.2* write the equation that best models the problem 5.2 CC.912.F.IF.7d (+)* sketch a graph of a rational function based on its domain, xintercepts, yintercept, and end behavior 5.3 CC.912.F.IF.7d (+)* use technology to graph rational functions 5.4 CC.912.A.APR.7 (+) multiply and divide rational expressions 5.5 CC.912.A.APR.7 (+) add and subtract rational expressions 5.6 CC.912.A.REI.2 solve a rational equation in one variable determine which numbers cannot be solutions of a radical equation and explain why 5.7 CC.912.F.IF.9 compare properties of two functions represented in different ways
6 6 Data Analysis and Statistics 6.1 Use Combinations and the Binomial Theorem 6.2 Construct and Interpret Binomial Distributions 6.3 Use Normal Distributions 6.4 Select and Draw Conclusions from Samples 6.5 Compare Surveys, Experiments, and Observational Studies 6.1 CC.912.A.APR.5 (+) apply the combination formula write the binomial expansion 6.2 CC.912.S.MD.3 (+)* define the random variable and construct a probability distribution table for possible values of the random variable 6.3 CC.912.S.ID.4* recognize that normal distributions are only appropriate for unimodal and symmetric shapes estimate the area under a normal curve 6.4 CC.912.S.IC.1* recognize that statistics involves drawing conclusions about a population based on the results obtained from a random sample of the population 6.5 CC.912.S.IC.3* describe the differences among sample surveys, experiments, and observational studies 7 Sequences and Series 7.1 Define and Use Sequences and Series 7.2 Analyze Arithmetic Sequences and Series 7.3 Analyze Geometric Sequences and Series 7.4 Find Sums of Infinite Geometric Series 7.5 Use Recursive Rules with Sequences and Functions 7.1 CC.912.F.IF.3 explain that a recursive formula tells how a sequence or series starts, and how to use the previous entry to generate the next entry 7.2 CC.912.F.BF.2* define an arithmetic sequence determine the common difference between two terms in an arithmetic sequence write a recursive rule for the arithmetic sequence 7.3 CC.912.A.SSE.4* define a finite geometric series and common ratio
7 7.4 CC.912.A.SSE.3* derive a formula for the sum of a finite and infinite geometric sequences series express the sum of a finite geometric series calculate the sum of a finite geometric series 7.5 CC.912.F.BF.2* explain that a recursive formula tells how a sequence starts and how to use the previous value to get the next element of the sequence 8 Quadratic Relations and Conic Sections 8.1 Apply the Distance and Midpoint Formulas 8.2 Graph and Write Equations of Parabolas 8.3 Graph and Write Equations of Circles 8.4 Graph and Write Equations of Ellipses 8.5 Graph and Write Equations of Hyperbolas 8.6 Translate and Classify Conic Sections 8.7 Solve Quadratic Systems 8.1 CC.912.G.GPE.4 use the distance and midpoint formula 8.2 CC.912.G.GPE.2 graph and write the equation of a parabola using the focus and directrix identify the focus and directrix 8.3 CC.912.G.GPE.1 graph and write the equation of a circle using the coordinates of the center, and its radius or diameter 8.4 CC.912.G.GPE.3 (+) define an ellipse identify the foci of an ellipse write and graph the equation of an ellipse identify the center, foci, axes, and asymptotes of a ellipse 8.5 CC.912.G.GPE.3 (+) define an hyperbola identify the foci of an hyperbola write and graph the equation of an hyperbola identify the center, foci, axes, and asymptotes of a hyperbola 8.6 CC.912.G.GPE.3 (+) identify elements in the equation to translate various conic sections 8.7 CC.912.A.REI.7 solve a system of quadratic equations using graphing, substitution or elimination
8 9 Trigonometric Ratios and Functions 9.1 Use Trigonometry with Right Triangles 9.2 Define General Angles and Use Radian Measure 9.3 Evaluate Trigonometric Functions of Any Angle 9.4 Evaluate Inverse Trigonometric Functions 9.5 Apply the Law of Sines 9.6 Apply the Law of Cosines 9.1 CC.912.G.SRT.6 use trigonometric ratios to identify sine, cosine and tangent 9.2 CC.912.F.TF.1 define the unit circle define the radian measure of an angle 9.3 CC.912.F.TF.2 label the unit circle in radians identify sine and cosine of an angle when given a graph of a unit circle with the labeled coordinates 9.4 CC.912.F.TF.6 (1) define inverse function explain why functions do not have inverses 9.5 CC.912.G.SRT.11 (1) apply the law of sines to find unknown side lengths and angle measures in right and nonright triangles 9.6 CC.912.G.SRT.11 (1) apply the law of cosines to find unknown side lengths and angle measures in right and nonright triangles 10 Trigonometric Graphs, Identities, and Equations 10.1 Graph Sine, Cosine, and Tangent Functions 10.2 Translate and Reflect Trigonometric Graphs 10.3 Verify Trigonometric Identities 10.4 Solve Trigonometric Equations 10.5 Write Trigonometric Functions and Models 10.6 Apply Sum and Difference Formulas 10.7 Apply DoubleAngle and HalfAngle Formulas 10.1 C.912.F.IF.7e* graph trigonometric functions showing period, midline and amplitude
9 10.2 CC.912.F.TF.5* define the amplitude, frequency, and midline of a trigonometric function 10.3 CC.912.F.TF.8 derive the Pythagorean identity by using the unit circle and definitions of sine and cosine and applying the Pythagorean Theorem 10.4 CC.912.F.TF.7(1)* solve trigonometric equations using inverse trigonometric functions 10.5 CC.912.F.TF.5* write a function notation for the trigonometric function that models a problem situation, given the amplitude, frequency (or period), and midline of a periodic situation 10.6 CC.912.F.TF.9(1) use the sum and difference formulas for sine, cosine, and tangent to solve for exact values of trigonometric functions of other angles use the sum and difference formulas for sine, and cosine to prove the sum and difference formulas for tangent 10.7 CC.912.F.TF.9(1) use the halfangle and double angle formulas to prove the addition and subtraction formulas for sine, cosine, and tangent and use them to solve the problems
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