Lesson Plan

Determine from $\Delta = b^2-4ac$, without solving, whether a quadratic has two distinct real, one repeated real, or two non-real roots, and whether real roots are rational or irrational

Relate the sign of $\Delta$ to the number of $x$-intercepts of the corresponding parabola

Translate a stated condition on the roots, including tangency of a line and a parabola, into a condition on $\Delta$ and solve for an unknown coefficient

Choose the discriminant over a full solve when a question asks only how many or what kind of roots exist

A 605. Solve quadratic equations A 601. Manipulate expressions and equations N 504. Exhibit some knowledge of the complex numbers N 604. Apply the facts that π is irrational and that the square root of an integer is rational only if that integer is a perfect square N 704. Apply properties of complex numbers and the complex number system AF 705. Identify characteristics of graphs based on a set of conditions or on a general equation such as y = ax² + c AF 703. Analyze and draw conclusions based on properties of algebra and/or functions