Math 20-1

- It is expected that students will: 1. Factor polynomial expressions of the form: ax2 + bx + c, a ≠ 0 - 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. Notes

- It is expected that students will: 3. Analyze quadratic functions of the form y = a(x – p)2 + q and determine the - Vertex - Domain and range - Direction of opening - Axis of symmetry

- It is expected that students will: 4. Analyze quadratic functions of the form y = ax2 + bx + c to identify characteristics of the corresponding graph, including - Vertex - Domain and range - Direction of opening - Axis of symmetry

- Solve problems that involve quadratic equations. [ICT: C6–4.1]

- Graph and analyze the reciprocals of linear and quadratic functions. [ICT: C6–4.1, C6–4.3] - Compare the graphs of y = f(x) and y = 1/f(x). - Identify x-values where y = 1/f(x) has vertical asymptotes and relate them to the non-permissible values of the related rational expression. - Graph y = 1/f(x) from a given linear or quadratic y = f(x), and graph y = f(x) from a given reciprocal graph; explain the strategies used.

- Graph and analyze absolute value functions (limited to linear and quadratic functions) to solve problems. [ICT: C6–4.1, C6–4.3]

- Model situations using systems of linear–quadratic or quadratic–quadratic equations in two variables. - Relate a given system to its problem context. - Determine and verify solutions for such systems algebraically and graphically (with technology). [ICT: C6–4.1, C6–4.4] - Explain the meaning of points of intersection and why such systems may have zero, one, two, or infinitely many solutions. - Solve problems involving these systems and justify the strategy used.

- Solve problems that involve linear and quadratic inequalities in two variables, excluding systems of linear inequalities. [ICT: C6–4.1, C6–4.3] - Use test points to determine the solution region of an inequality. - Explain when to use a solid versus a broken boundary line. - Sketch the graph of a linear or quadratic inequality, with or without technology. - Create an inequality to model a given problem, and solve and interpret the result.

- Solve problems that involve quadratic inequalities in one variable. - 1 Determine the solution of a quadratic inequality in one variable using strategies such as sign analysis, case analysis, graphing, or roots and test points, and explain the strategy used. - 2 Represent and solve a problem that involves a quadratic inequality in one variable. - 3 Interpret the solution to a problem that involves a quadratic inequality in one variable.