A-REI.2.4.b

Solve quadratic equations in one variable.

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.

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Formative Assessments
Formative Assessments
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Students are asked to derive the quadratic formula by completing the square.
Quadratic Formula – 1
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Students are asked to complete the derivation of the quadratic formula.
Quadratic Formula – 2
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Students are shown four quadratic equations and asked to choose the best method for solving each equation.
Which Strategy?
Virtual/Hands-on Manipulatives
Virtual/Hands-on Manipulatives
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This resource can be used to assess students' understanding of solving quadratic equation by taking the square root. A great resource to view prior to this is ``Solving quadratic equations by square root' by Khan Academy.
Solving Quadratics By Taking The Square Root
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Assessment Questions
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Hook/Performance Tasks
Hook/Performance Tasks
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This classroom task is meant to elicit a variety of different methods of solving a quadratic equation (A-REI.4). Some are straightforward (for example, expanding the square on the right and rearranging the equation so that we can use the quadratic formula); some are simple but clever (reasoning from the fact that x and (2x - 9) have the same square); some use tools (using a graphing calculator to graph the functions f(x) = x^2 and g(x) = (2x-90)^2 and looking for values of x at which the two functions intersect). Some solution methods will work on an arbitrary quadratic equation, while others (such as the last three) may have difficulty or fail if the quadratic equation is not given in a particular form, or if the solutions are not rational numbers.
Two Squares are Equal
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The problem presents a context where a quadratic function arises. Careful analysis, including graphing of the function, is closely related to the context. The student will gain valuable experience applying the quadratic formula and the exercise also gives a possible implementation of completing the square.
Springboard Dive
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This task provides an exploration of a quadratic equation by descriptive, numerical, graphical, and algebraic techniques. Based on its real-world applicability, teachers could use the task as a way to introduce and motivate algebraic techniques like completing the square, en route to a derivation of the quadratic formula.
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