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Skills available for Louisiana high school math standards

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Louisiana Student Standards (adopted in 2025): Algebra I Louisiana Student Standards (adopted in 2025): Algebra I
Louisiana Student Standards (adopted in 2025): Algebra II Louisiana Student Standards (adopted in 2025): Algebra II
Louisiana Student Standards (adopted in 2025): Geometry Louisiana Student Standards (adopted in 2025): Geometry
Louisiana Student Standards (adopted in 2025): Integrated Math I Louisiana Student Standards (adopted in 2025): Integrated Math I
Louisiana Student Standards (adopted in 2025): Integrated Math II Louisiana Student Standards (adopted in 2025): Integrated Math II
Louisiana Student Standards (adopted in 2025): Integrated Math III Louisiana Student Standards (adopted in 2025): Integrated Math III
Louisiana Student Standards: Algebra I Louisiana Student Standards: Algebra I
Louisiana Student Standards: Algebra II Louisiana Student Standards: Algebra II
Louisiana Student Standards: Geometry Louisiana Student Standards: Geometry
Louisiana Student Standards: Mathematical Practices Louisiana Student Standards: Mathematical Practices

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I2:N Number & Quantity

I2:N-RN Number and Quantity: The Real Number System
- I2:N-RN.A Extend the properties of exponents to rational exponents.
  - I2:N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.
  - I2:N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.
- I2:N-RN.B Use properties of rational and irrational numbers.
  - I2:N-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.
  - Checkpoint opportunity
    - Checkpoint: Radicals and rational exponents (A1-EE.10)
I2:N-CN The Complex Number System
- I2:N-CN.A Perform arithmetic operations with complex numbers.
  - I2:N-CN.A.1 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.
    - Introduction to complex numbers (A2-K.1)
  - I2:N-CN.A.2 Use the relation i²= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.
- I2:N-CN.C Use complex numbers in polynomial identities and equations. Limit to quadratics with real coefficients.
  - I2:N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.
    - Solve a quadratic equation using square roots (A2-O.1)
    - Using the discriminant (A2-O.8)
  - I2:N-CN.C.8 Extend polynomial identities to the complex numbers.
    - Complex conjugate theorem (A2-Q.7)
    - Conjugate root theorems (A2-Q.8)
  - I2:N-CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

I2:A Algebra

I2:A-SSE Seeing Structure in Expressions
- I2:A-SSE.A Interpret the structure of expressions.
  - I2:A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.
    - I2:A-SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients.
    - I2:A-SSE.A.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.
      - Interpret parts of quadratic expressions: word problems (A1-Y.15)
  - I2:A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it for a specific purpose.
- I2:A-SSE.B Write expressions in equivalent forms to solve problems.
  - I2:A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.
    - I2:A-SSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines.
    - I2:A-SSE.B.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.
    - I2:A-SSE.B.3c Use the properties of exponents to transform expressions for exponential functions, emphasizing integer exponents.
      - Evaluate expressions using exponent rules (A1-R.12)
  - Checkpoint opportunity
    - Checkpoint: Quadratic and exponential expressions (A1-AA.14)
I2:A-APR Arithmetic with Polynomials and Rational Expressions
- I2:A-APR.A Perform arithmetic operations on polynomials.
  - I2:A-APR.A.1 Understand that polynomials form a system comparable to the integers, as they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
  - Checkpoint opportunity
    - Checkpoint: Polynomial operations (A1-W.16)
I2:A-CED Creating Equations
- I2:A-CED.A Create equations that describe numbers or relationships.
  - I2:A-CED.A.1 Create equations and inequalities and use them to solve problems. Include equations arising from linear, quadratic, and exponential situation functions.
  - I2:A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
  - I2:A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.
  - I2:A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Include formulas involving quadratic terms.
    - Rearrange multi-variable equations (A2-B.4)
I2:A-REI Reasoning with Equations and Inequalities
- I2:A-REI.B Solve equations and inequalities in one variable.
  - I2:A-REI.B.4 Solve quadratic equations in one variable.
    - I2:A-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.
      - Complete the square (A1-Z.4)
    - I2:A-REI.B.4b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.
    - I2:A-REI.B.4c Recognize when the quadratic formula gives complex solutions and write them as "no real solution."
      - Using the discriminant (A1-Z.8)
- I2:A-REI.C Solve systems of equations.
  - I2:A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.
    - Solve a system of linear and quadratic equations by graphing (A1-Z.9)
    - Solve a system of linear and quadratic equations (A1-Z.10)
  - Checkpoint opportunity
    - Checkpoint: Quadratic equations (A1)

I2:F Functions

I2:F-IF Functions: Interpreting Functions
- I2:F-IF.B Interpret quadratic functions that arise in applications in terms of the context.
  - I2:F-IF.B.4 For a function that models a relationship between two quantities.
    - I2:F-IF.B.4a Interpret key features of graphs and tables in terms of the quantities.
    - I2:F-IF.B.4b Sketch graphs showing key features given a verbal description of the relationship.
      - Identify graphs: word problems (A1-M.14)
    - I2:F-IF.B.4c Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums, symmetries and end behavior.
  - I2:F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.
  - I2:F-IF.B.6 Calculate and interpret the average rate of change of a quadratic function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.
    - Rate of change: tables (A1-M.15)
    - Rate of change: graphs (A1-M.16)
- I2:F-IF.C Analyze linear, exponential, quadratic, absolute value, step, and piecewise-defined functions using different representations.
  - I2:F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.
    - I2:F-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.
    - I2:F-IF.C.7b Graph piecewise linear (to include absolute value) and exponential functions.
  - I2:F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
    - I2:F-IF.C.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.
  - I2:F-IF.C.9 Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential), each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).
    - Compare linear functions: graphs and equations (A1-N.11)
    - Compare linear functions: tables, graphs, and equations (A1-N.12)
  - Checkpoint opportunity
    - Checkpoint: Interpret features of functions (A1)
    - Checkpoint: Graph and analyze functions (A1)
I2:F-BF Building Functions
- I2:F-BF.A Build a function that models a relationship between two quantities.
  - I2:F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relationship between two quantities.
    - I2:F-BF.A.1a Determine an explicit expression or steps for calculation from a context.
    - I2:F-BF.A.1b Combine standard function types using arithmetic operations.
- I2:F-BF.B Build new functions from existing functions.
  - I2:F-BF.B.3 Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative). Without technology, find the value of k given the graphs of linear and quadratic functions. With technology, experiment with cases and illustrate an explanation of the effects on the graph that include cases where f(x) is a linear, quadratic, piecewise linear (to include absolute value), or exponential function.
  - I2:F-BF.B.4 Find inverse functions: Solve an equation of the form f(x) = c for a simple function f that has an inverse; Write an expression for the inverse.
    - Find the inverse of a linear function (A1-CC.3)
I2:F-LE Linear, Quadratic, and Exponential Models
- I2:F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.
  - I2:F-LE.A.3 Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically, with and without technology.
    - Compare linear, exponential, and quadratic growth (A1-AA.12)
I2:F-TF Trigonometric Functions
- I2:F-TF.C Prove and apply trigonometric identities.
  - I2:F-TF.C.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find the value of sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.
    - Find trigonometric ratios using a Pythagorean or reciprocal identity (A2-MM.3)
    - Find trigonometric ratios using multiple identities (A2-MM.4)

I2:G Geometric Reasoning & Logic

I2:G-CO Congruence
- I2:G-CO.C Prove and apply geometric theorems.
  - I2:G-CO.C.3 Prove and apply theorems about lines and angles. Theorems include but are not limited to: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
  - I2:G-CO.C.4 Prove and apply theorems about triangles. Theorems include but are not limited to: measures of interior angles of a triangle sum to 180°; base angles of isosceles triangles are congruent; the segment joining midpoints of two sides of a triangle is parallel to the third side and half the length; the medians of a triangle meet at a point.
  - I2:G-CO.C.5 Prove and apply theorems about parallelograms. Theorems include but not limited to: opposite sides are congruent; opposite angles are congruent; the diagonals of a parallelogram bisect each other, and the converse of this theorem; rectangles are parallelograms with congruent diagonals and the converse of this theorem.
  - Checkpoint opportunity
I2:G-SRT Similarity, Right Triangles, and Trigonometry
- I2:G-SRT.A Understand similarity in terms of similarity transformations.
  - I2:G-SRT.A.1 Verify experimentally the properties of dilations given by a center and a scale factor:
    - I2:G-SRT.A.1a A dilation takes a line not passing through the center of the dilation to a parallel line, and leaves a line passing through the center unchanged.
      - Dilations: graph the image (G-I.1)
      - Dilations and parallel lines (G-I.7)
    - I2:G-SRT.A.1b The dilation of a line segment is longer or shorter in the ratio given by the scale factor.
  - I2:G-SRT.A.2 Using similarity transformations: Determine if two figures are similar using the definition of similarity transformations; Explain the meaning of similarity for triangles as the equality of all corresponding pairs of angles and proportionality of all corresponding sides.
  - I2:G-SRT.A.3 Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar.
    - Similarity rules for triangles (G-M.8)
  - Checkpoint opportunity
    - Checkpoint: Dilations (G-I.9)
    - Checkpoint: Similarity transformations (G-M.18)
- I2:G-SRT.B Prove and apply theorems involving similarity.
  - I2:G-SRT.B.4 Prove and apply theorems about triangles. Theorems include but not limited to: a line parallel to one side of a triangle divides the other two proportionally, and the converse of this theorem; the Pythagorean Theorem proved using triangle similarity; SAS similarity criteria; SSS similarity criteria; AA similarity criteria.
  - I2:G-SRT.B.5 Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.
  - Checkpoint opportunity
    - Checkpoint: Triangle similarity and congruence (G-M.19)
- I2:G-SRT.C Define trigonometric ratios and solve problems involving right triangles.
  - I2:G-SRT.C.6 Understand that by similarity, side ratios in right triangles, including special right triangles (30–60–90 and 45–45–90), are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
  - I2:G-SRT.C.7 Explain and use the relationship between the sine and cosine of complementary angles.
    - Sine and cosine of complementary angles (G-Q.9)
  - I2:G-SRT.C.8 Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.
  - Checkpoint opportunity
    - Checkpoint: Right triangle trigonometry (G-Q.16)
I2:G-C Circles
- I2:G-C.A Understand and apply theorems about circles.
  - I2:G-C.A.1 Understand that all circles are similar.
    - Similarity of circles (G-M.11)
  - I2:G-C.A.2 Identify and describe relationships among inscribed angles, radii, and chords, including the following: the relationship that exists between central, inscribed, and circumscribed angles; inscribed angles on a diameter are right angles; and a radius of a circle is perpendicular to the tangent where the radius intersects the circle.
  - I2:G-C.A.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
  - I2:G-C.A.4 Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
  - Checkpoint opportunity
    - Checkpoint: Prove circles are similar (G-M.20)
    - Checkpoint: Angles and lines in circles (G-W.18)
- I2:G-C.B Find arc lengths and areas of sectors of circles.
  - I2:G-C.B.5 Apply the formula for finding area of a sector and arc length. (Radians are introduced only as a unit of measure.)
  - Checkpoint opportunity
    - Checkpoint: Arc length and area of sectors (G-W.20)
I2:G-GPE Expressing Geometric Properties with Equations
- I2:G-GPE.A Translate between the geometric description and the equation for a conic section.
  - I2:G-GPE.A.1 Derive the equation of a circle of given center and radius using the Pythagorean Theorem; complete the square to find the center and radius of a circle given by an equation.
  - I2:G-GPE.A.2 Derive the equation of a parabola given a focus and directrix.
  - Checkpoint opportunity
    - Checkpoint: Equations of circles (G-Y.11)
    - Checkpoint: Equations of parabolas (G-Z.10)
- I2:G-GPE.B Use coordinates to prove simple geometric theorems algebraically.
  - I2:G-GPE.B.4 Use coordinates to prove geometric theorems algebraically.
    - Classify shapes on the coordinate plane: justify your answer (G-O.13)
    - Determine if a point lies on a circle (G-Y.3)
  - Checkpoint opportunity
    - Checkpoint: Coordinate proofs (G-E.8)
I2:G-MD Geometric Measurement and Dimension
- I2:G-MD.A Explain volume formulas and use them to solve problems.
  - I2:G-MD.A.1 Give an informal argument for the formulas of: circumference of a circle; area of a circle; and volume of a cylinder, pyramid, and cone.
  - I2:G-MD.A.3 Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.
  - Checkpoint opportunity
    - Checkpoint: Volume (G-U.19)
I2:S-CP Conditional Probability and the Rules of Probability
- I2:S-CP.A Understand independence and conditional probability and use them to interpret data.
  - I2:S-CP.A.1 Describe events as subsets of a sample space (the set of outcomes) using characteristics (or categories) of the outcomes, or as unions, intersections, or complements of other events ("or," "and," "not").
    - Theoretical and experimental probability (G-AA.1)
    - Outcomes of compound events (G-AA.2)
  - I2:S-CP.A.2 Understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities, and use this characterization to determine if they are independent.
  - I2:S-CP.A.3 Understand the conditional probability of A given B as ^{P(A and B)}/_P(B), and interpret independence of A and B as saying that the conditional probability of A given B is the same as the probability of A, and the conditional probability of B given A is the same as the probability of B.
    - Find conditional probabilities (G-AA.11)
    - Independence and conditional probability (G-AA.13)
  - I2:S-CP.A.4 Construct and interpret two-way frequency tables of data when two categories are associated with each object being classified. Use the two-way table as a sample space to decide if events are independent and to approximate conditional probabilities.
  - I2:S-CP.A.5 Recognize and explain the concepts of conditional probability and independence in everyday language and everyday situations.
    - Identify independent events (G-AA.10)
    - Independence and conditional probability (G-AA.13)
- I2:S-CP.B Use the rules of probability to compute probabilities of compound events in a uniform probability model.
  - I2:S-CP.B.6 Find the conditional probability of A given B as the fraction of B's outcomes that also belong to A, and interpret the answer in terms of the model.
  - I2:S-CP.B.7 Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B), and interpret the answer in terms of the model.
    - Find probabilities using the addition rule (G-AA.15)
  - I2:S-CP.B.8 Apply the general Multiplication Rule in a uniform probability model, P(A and B) = P(A)P(B|A) = P(B)P(A|B), and interpret the answer in terms of the model.
    - Find conditional probabilities (G-AA.11)
  - I2:S-CP.B.9 Understand and apply the concepts of permutations and combinations: Use permutations and combinations to compute probabilities of compound events and solve problems.
  - Checkpoint opportunity
    - Checkpoint: Understand independence and conditional probability (G-AA.16)
    - Checkpoint: Probabilities of compound events (G-AA.17)
I2:S-MD Using Probability to Make Decisions
- I2:S-MD.B Use probability to evaluate outcomes of decisions.
  - I2:S-MD.B.6 Use probabilities to make fair decisions (drawing by lots, using a random number generator, etc).
  - I2:S-MD.B.7 Analyze decisions and strategies using probability concepts.

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I2:N Number & Quantity

I2:N-RN Number and Quantity: The Real Number System

I2:N-RN.A Extend the properties of exponents to rational exponents.

I2:N-RN.A.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents.

I2:N-RN.A.2 Rewrite expressions involving radicals and rational exponents using the properties of exponents.

I2:N-RN.B Use properties of rational and irrational numbers.

I2:N-RN.B.3 Explain why the sum or product of two rational numbers is rational; that the sum of a rational number and an irrational number is irrational; and that the product of a nonzero rational number and an irrational number is irrational.

Checkpoint opportunity

I2:N-CN The Complex Number System

I2:N-CN.A Perform arithmetic operations with complex numbers.

I2:N-CN.A.1 Know there is a complex number i such that i2 = –1, and every complex number has the form a + bi with a and b real.

I2:N-CN.A.2 Use the relation i2= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

I2:N-CN.C Use complex numbers in polynomial identities and equations. Limit to quadratics with real coefficients.

I2:N-CN.C.7 Solve quadratic equations with real coefficients that have complex solutions.

I2:N-CN.C.8 Extend polynomial identities to the complex numbers.

I2:N-CN.C.9 Know the Fundamental Theorem of Algebra; show that it is true for quadratic polynomials.

I2:A Algebra

I2:A-SSE Seeing Structure in Expressions

I2:A-SSE.A Interpret the structure of expressions.

I2:A-SSE.A.1 Interpret expressions that represent a quantity in terms of its context.

I2:A-SSE.A.1a Interpret parts of an expression, such as terms, factors, and coefficients.

I2:A-SSE.A.1b Interpret complicated expressions by viewing one or more of their parts as a single entity.

I2:A-SSE.A.2 Use the structure of an expression to identify ways to rewrite it for a specific purpose.

I2:A-SSE.B Write expressions in equivalent forms to solve problems.

I2:A-SSE.B.3 Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

I2:A-SSE.B.3a Factor a quadratic expression to reveal the zeros of the function it defines.

I2:A-SSE.B.3b Complete the square in a quadratic expression to reveal the maximum or minimum value of the function it defines.

I2:A-SSE.B.3c Use the properties of exponents to transform expressions for exponential functions, emphasizing integer exponents.

Checkpoint opportunity

I2:A-APR Arithmetic with Polynomials and Rational Expressions

I2:A-APR.A Perform arithmetic operations on polynomials.

I2:A-APR.A.1 Understand that polynomials form a system comparable to the integers, as they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.

Checkpoint opportunity

I2:A-CED Creating Equations

I2:A-CED.A Create equations that describe numbers or relationships.

I2:A-CED.A.1 Create equations and inequalities and use them to solve problems. Include equations arising from linear, quadratic, and exponential situation functions.

I2:A-CED.A.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.

I2:A-CED.A.3 Represent constraints by equations or inequalities, and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context.

I2:A-CED.A.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Include formulas involving quadratic terms.

I2:A-REI Reasoning with Equations and Inequalities

I2:A-REI.B Solve equations and inequalities in one variable.

I2:A-REI.B.4 Solve quadratic equations in one variable.

I2:A-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions.

I2:A-REI.B.4b Solve quadratic equations by inspection, taking square roots, completing the square, the quadratic formula, and factoring, as appropriate to the initial form of the equation.

I2:A-REI.B.4c Recognize when the quadratic formula gives complex solutions and write them as "no real solution."

I2:A-REI.C Solve systems of equations.

I2:A-REI.C.7 Solve a simple system consisting of a linear equation and a quadratic equation in two variables algebraically and graphically.

Checkpoint opportunity

I2:F Functions

I2:F-IF Functions: Interpreting Functions

I2:F-IF.B Interpret quadratic functions that arise in applications in terms of the context.

I2:F-IF.B.4 For a function that models a relationship between two quantities.

I2:F-IF.B.4a Interpret key features of graphs and tables in terms of the quantities.

I2:F-IF.B.4b Sketch graphs showing key features given a verbal description of the relationship.

I2:F-IF.B.4c Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums, symmetries and end behavior.

I2:F-IF.B.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes.

I2:F-IF.B.6 Calculate and interpret the average rate of change of a quadratic function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.

I2:F-IF.C Analyze linear, exponential, quadratic, absolute value, step, and piecewise-defined functions using different representations.

I2:F-IF.C.7 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.

I2:F-IF.C.7a Graph linear and quadratic functions and show intercepts, maxima, and minima.

I2:F-IF.C.7b Graph piecewise linear (to include absolute value) and exponential functions.

I2:F-IF.C.8 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

I2:F-IF.C.8a Use the process of factoring and completing the square in a quadratic function to show zeros, extreme values, and symmetry of the graph, and interpret these in terms of a context.

I2:F-IF.C.9 Compare properties of two functions (linear, quadratic, piecewise linear [to include absolute value] or exponential), each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions).

Checkpoint opportunity

I2:F-BF Building Functions

I2:F-BF.A Build a function that models a relationship between two quantities.

I2:F-BF.A.1 Write a linear, quadratic, or exponential function that describes a relationship between two quantities.

I2:F-BF.A.1a Determine an explicit expression or steps for calculation from a context.

I2:F-BF.A.1b Combine standard function types using arithmetic operations.

I2:F-BF.B Build new functions from existing functions.

I2:F-BF.B.4 Find inverse functions: Solve an equation of the form f(x) = c for a simple function f that has an inverse; Write an expression for the inverse.

I2:F-LE Linear, Quadratic, and Exponential Models

I2:F-LE.A Construct and compare linear, quadratic, and exponential models and solve problems.

I2:F-LE.A.3 Observe, using graphs and tables, that a quantity increasing exponentially eventually exceeds a quantity increasing linearly or quadratically, with and without technology.

I2:F-TF Trigonometric Functions

I2:F-TF.C Prove and apply trigonometric identities.

I2:N-CN.A.1 Know there is a complex number i such that i² = –1, and every complex number has the form a + bi with a and b real.

I2:N-CN.A.2 Use the relation i²= –1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

I2:A-REI.B.4a Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)² = q that has the same solutions.

I2:F-TF.C.8 Prove the Pythagorean identity sin²(θ) + cos²(θ) = 1 and use it to find the value of sin(θ), cos(θ), or tan(θ) given sin(θ), cos(θ), or tan(θ) and the quadrant of the angle.