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 in Algebra I 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 (The discriminant is a sufficient way to recognize when the process yields no real solutions).
Recognize when the process yields no real solutions.
Solutions may include simplifying radicals or writing solutions in simplest radical form.

AII/PRECALCULUS

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. Derive the quadratic formula from this form. b. Solve quadratic equations by inspection (e.g., for x²=49), taking square roots, completing the square, the quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize when the quadratic formula gives complex solutions and write them as a ± bi for real numbers a and b.

AI

AII

PRECALCULUS

AI

Practice-Solving Quadratics 4
taking square roots

Practice-Solving Quadratics 6
factoring

Practice-Solving Quadratics 7
factoring

Practice-Solving Quadratics 11
factoring

Practice-Solving Quadratics 5
factoring

Practice-Solving Quadratics 1
completing the square

Practice-Solving Quadratics 2
completing the square

Practice-Solving Quadratics 3
completing the square

Practice-Solving Quadratics 8
quadratic formula

Practice-Solving Quadratics 9
quadratic formula

Practice-Solving Quadratics 10
quadratic formula

Practice-Solving Quadratics 12
quadratic formula

Practice-Using the Discriminant 1

Journal-Solving Quadratics
taking square roots, factoring, completing the square, quadratic formula

Journal-Using the Discriminant