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Solving Quadratic Equations (D) - By Completing the Square WORKSHEET
Suitable for Grades: Algebra I, IM 1
CCSS: HSA.REI.B.4, HSA.REI.B.4.B
CCSS Description: 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.
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.
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.
Solving Quadratic Equations (D) - By Completing the Square WORKSHEET DESCRIPTION
This worksheet is designed to provide a scaffolded approach to solving quadratic equations by completing the square. Section A provides four quadratic equations that have already been written in the completed square from and just need to be rearranged to give the solutions for x. Section B then presents some quadratic equations with an x squared coefficient of one, four of which are equal to zero, and four of which require additional manipulation. Section C then provides six quadratic equations with an x squared coefficient greater than one. For an extra challenge, the extension question asks learners to find missing coefficients and also derive the quadratic formula.
