3.RF5 Solve problems that involve quadratic equations.
3.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.
3.RF5.2 Solve a quadratic equation of the form ax² + bx + c = 0 by using strategies such as:
3.RF5.3 Derive the quadratic formula, using deductive reasoning.
3.RF5.4 Identify and correct errors in a solution to a quadratic equation.
3.RF5.5 Select a method for solving a quadratic equation, justify the choice, and verify the solution.
3.RF5.6 Explain, using examples, how the discriminant may be used to determine whether a quadratic equation has two, one, or no real (i.e., imaginary) roots; and relate the number of zeros to the graph of the corresponding quadratic function.
5.AN4 Determine equivalent forms of rational expressions (limited to numerators and denominators that are monomials, binomials or trinomials).
5.AN4.1 Explain why a given value is non-permissible for a given rational expression.
5.AN4.2 Determine the non-permissible values for a rational expression.
5.AN4.3 Compare the strategies for writing equivalent forms of rational expressions to the strategies for writing equivalent forms of rational numbers.
5.AN4.4 Determine a rational expression that is equivalent to a given rational expression by multiplying the numerator and denominator by the same factor (limited to a monomial or a binomial), and state the non-permissible values of the equivalent rational expression.
6.RF11 Graph and analyze reciprocal functions (limited to the reciprocal of linear and quadratic functions).
6.RF11.1 Compare the graph of y= 1/f(x) to the graph of y = f(x).
6.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 non-permissible values of the related rational expression.