11.RF5 Solve problems that involve quadratic equations.
11.RF5.1 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.
11.RF5.2 Solve a quadratic equation of the form ax² + bx + c = 0 by using strategies such as:
11.RF5.3 Derive the quadratic formula, using deductive reasoning.
11.RF5.4 Identify and correct errors in a solution to a quadratic equation.
11.RF5.5 Select a method for solving a quadratic equation, justify the choice, and verify the solution.
11.RF5.6 Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real roots; and relate the number of zeros to the graph of the corresponding quadratic function.
11.RF11 Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
11.RF11.1 Compare the graph of y = 1/f(x) to the graph of y = f(x).
11.RF11.2 Identify, given a function f(x), values of x for which y = 1/f(x) will have vertical asymptotes; and describe their relationship to the nonpermissible values of the related rational expression.