STANDARD A.REI.B.4
AI

Solve quadratic equations in one variable.
a. Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x-p)2=q that has the same solutions. Understand that the quadratic formula is a derivative of this process. When utilizing the method of completing the square, the quadratic's leading coefficient will be 1 and the coefficient of the linear term will be limited to even (after the possible factoring out of a GCF). Students should be able to complete the square in which manipulating the given quadratic equation yields an integer value for q.
b. Solve quadratic equations by:  i) inspection (An example for inspection would be x2=49, where a student should know that the solutions would include 7 and -7), ii) taking square roots, iii) factoring, iv) completing the square, v) the quadratic formula (When utilizing the quadratic formula, there are no coefficient limits), and vi) graphing.
Recognize when the process yields no real solutions.  The discriminant is a sufficient way to recognize when the process yields no real solutions.
Solutions may include simplifying radicals or writing solutions in simplest radical form.

AII

Solve quadratic equations in one variable.
b. Solve quadratic equations by:  i) inspection (An example for inspection would be x2=-81, where a student should know that the solutions would include 9i and -9i), ii) taking square roots, iii) factoring, iv) completing the square (An example where students need to factor out a leading coefficient while completing the square would be 4x2+8x-9=0), v) the quadratic formula, and vi) graphing.
Write complex solutions in a+bi form.