Students determine whether a relation defined by a graph, a set of ordered pairs, or symbolic expression is a function and justify the conclusion. Students know the quadratic formula and are familiar with its proof by completing the square. Students use the quadratic formula to find the roots of a second degree polynomial and to solve quadratic equations. Students graph quadratic functions and know that their roots are the x-intercepts. Students apply quadratic equations to physical problems, such as the motion of an object under the force of gravity.
Students use and know simple aspects of a logical argument.
Students explain the difference between inductive and deductive reasoning and identify and provide examples of each. Students identify the hypothesis and conclusion in logical deduction. Students use counterexamples to show that an assertion is false and recognize that a single counterexample is sufficient to refute an assertion. Students use properties of the number system to judge the validity of results, to justify each step of a procedure and to prove or disprove statements. Students judge the validity of an argument based on whether the properties of the real number system and order of operations have been applied correctly at each step.