M.3HS.18 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x ²+ y²)² = (x² – y²)² + (2xy)² can be used to generate Pythagorean triples.
M.3HS.19 Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal's Triangle.
Represent and solve equations and inequalities graphically.
M.3HS.23 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values or find successive approximations. Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential and logarithmic functions.
Analyze functions using different representations.
M.3HS.24 Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases. Graph polynomial functions, identifying zeros when suitable factorizations are available and showing end behavior.
TGT Trigonometry of General Triangles and Trigonometric Functions
Apply trigonometry to general triangles.
M.3HS.25 Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
M.3HS.33 Represent constraints by equations or inequalities and by systems of equations and/or inequalities and interpret solutions as viable or non-viable options in a modeling context. (e.g., Represent inequalities describing nutritional and cost constraints on combinations of different foods.)
M.3HS.39 Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
M.3HS.40 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). (e.g., Given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.)
M.3HS.48 Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost and/or working with typographic grid systems based on ratios).