#### P20.1: Demonstrate understanding of the absolute value of real numbers and equations and functions involving the absolute value of linear and quadratic functions.

P20.1.b: Determine the distance of two real numbers of the form ±a, a! R, from 0 on a number line, and relate this to the absolute value of a (|a|).

P20.1.c: Determine the absolute value of a real number.

P20.1.d: Order, with justification, a set of real numbers that includes the absolute value of one or more of the quantities.

P20.1.h: Analyze, describe, and explain the relationship between the graph of y = f(x) and y = |f(x)|.

P20.1.k: Develop and apply strategies for determining the intercepts, domain, and range of y = |f(x)| given the equation of the function or its graph.

P20.1.l: Explain what the range of the function y = |f(x)| reveals about the graph of the function.

P20.1.m: Develop, generalize, explain, and apply strategies for graphically determining (with and without the use of technology) the solution set of an equation involving absolute values of algebraic expressions.

P20.1.n: Develop, generalize, explain, and apply strategies for algebraically determining the solution set of an equation involving absolute values of algebraic expressions.

P20.1.o: Analyze and generalize conclusions about absolute value inequalities of the form |f(x)| < 0.

P20.1.q: Solve situational questions involving absolute value functions or equations.

#### P20.2: Expand and demonstrate understanding of radicals with numerical and variable radicands including: computations, solving equations (limited to square roots and one or two radicals).

P20.2.a: Develop, generalize, explain, and apply strategies for expressing an entire radical (with numerical or variable radicand) as a mixed radical.

P20.2.b: Develop, generalize, explain, and apply strategies for expressing a mixed radical (with numerical or variable radicand) as an entire radical.

P20.2.d: Develop, generalize, explain, and apply strategies for simplifying radical expressions (with numerical and/or variable radicands).

P20.2.i: Develop, explain, and apply strategies for determining the values of a variable for which a given radical expression is defined.

P20.2.j: Develop, explain, and apply strategies for determining nonpermissible values (restrictions on values) for the variable in a radical equation.

P20.2.k: Develop, explain, and apply algebraic strategies for determining and verifying the roots of a radical equation.

P20.2.l: Explain why some roots determined in solving a radical equation are extraneous.

#### P20.4: Expand and demonstrate understanding of the primary trigonometric ratios including the use of reference angles (0° ? ? ? 360°) and the determination of exact values for trigonometric ratios.

P20.4.d: Determine the reference angle for an angle in standard position.

P20.4.l: Develop, explain, and apply strategies for solving, for all values of ?, equations of the form sin ? = a or cos ? =a, where ?1 ? a ? 1, and equations of the form tan ? = a, where a is a real number.

P20.4.m: Analyze 30°- 60°- 90° and 45°- 45°- 90° triangles to generalize about the relationship between pairs of sides in such triangles in relation to the angles.

P20.4.n: Develop, generalize, explain, and apply strategies for determining the exact value of the sine, cosine, or tangent (without the use of technology) of an angle with a reference angle of 30°, 45°, or 60°.

P20.4.o: Describe and generalize the relationships and patterns in and among the values of the sine, cosine, and tangent ratios for angles from 0° to 360°.

P20.4.p: Create and solve a situational question relevant to one?s self, family, or community which involves a trigonometric ratio.

#### P20.6: Expand and demonstrate understanding of factoring polynomial expressions including those of the form: a²x² - b²y², a ? 0, b ? 0; a(f(x))² - b(f(x)) + c, a ? 0; a²(f(x))² - b²(g(y))², a ? 0, b ? 0 where a, b, and c are rational numbers.

P20.6.a: Develop, generalize, explain, and apply strategies for factoring polynomial expressions of the form:

P20.6.a.1: a²x² - b²y², a ? 0, b ? 0, a and b are real numbers

P20.6.a.2: ca²x² - cb²y², a ? 0, b ? 0, a, b, and c are real numbers

P20.6.b: Verify, with explanation, whether or not a given binomial is a factor for a given polynomial.

#### P20.7: Demonstrate understanding of quadratic functions of the form y = ax² + bx + c and of their graphs, including: vertex, domain and range, direction of opening, axis of symmetry, x- and y-intercepts.

P20.7.d: Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of the function f(x) = a(x-p)² + q without the use of technology.

P20.7.e: Develop, explain, and apply strategies for graphing functions of the form f(x) = a(x - p)² + q by applying transformations related to the values of a, p, and q.

P20.7.f: Develop, explain, and apply strategies (that do not require graphing or the use of technology) for determining whether a quadratic function will have zero, one, or two x-intercepts.

P20.7.h: Develop, generalize, explain, verify, and apply a strategy (including completing the square) for writing a quadratic function in the form y = ax² + bx + c in the form y = a(x - p)² + q.

P20.7.j: Develop, generalize, explain, and apply strategies for determining the coordinates of the vertex, the domain and range, the axis of symmetry, x- and y- intercepts, and direction of opening of the graph of a function in the form y = ax² + bx + c.

P20.7.l: Write a quadratic function that models a given situation and explain any assumptions made.

P20.7.m: Analyze quadratic functions (with or without the use of technology) to answer situational questions.

#### P20.8: Demonstrate understanding of quadratic equations including the solution of: single variable equations, systems of linear-quadratic and quadratic-quadratic equations in two variables.

P20.8.a: Explain, using examples, the relationship among the roots of a quadratic equation, the zeros of the corresponding quadratic function and the x-intercepts of the graph of the quadratic function.

P20.8.c: Apply strategies for solving quadratic equations of the form ax² + bx + c = 0 including:

P20.8.c.2: factoring

P20.8.c.3: completing the square

P20.8.c.4: applying the quadratic formula

P20.8.c.5: graphing its corresponding function, with and without the use of technology.

P20.8.e: Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate this knowledge to the number of zeros that the corresponding quadratic function will have.

#### P20.9: Expand and demonstrate understanding of inequalities including: one-variable quadratic inequalities, two-variable linear and quadratic inequalities.

P20.9.a: Develop, generalize, explain, and apply strategies for determining the solution region for two-variable linear or two-variable quadratic inequalities.

P20.9.c: Explain, using examples, when a solid or broken line should be used in the graphic solution of a two-variable inequality.

P20.9.d: Explain what the solution region for a two-variable inequality means.

P20.9.e: Solve a situational question that involves a two-variable inequality.

#### P20.10: Demonstrate understanding of arithmetic and geometric (finite and infinite) sequences and series.

P20.10.a: Identify assumptions made in determining that a sequence or series is either arithmetic or geometric.

P20.10.c: Provide an example of an arithmetic or geometric sequence that is relevant to one?s self, family, or community.

P20.10.e: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, d, n, or tn in situational questions that involve arithmetic sequences.

P20.10.f: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, d, n, or Sn in situational questions that involve arithmetic series.

P20.10.g: Solve situational questions that involve arithmetic sequences and series.

P20.10.h: Develop, generalize, explain, and apply a rule and other strategies for determining the values of t?, a, r, n, or tn in situational questions that involve geometric sequences.

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this province's curriculum standards. Click any Gizmo title below for more information.