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[DOC File]Algebra II Standards Map - Instructional Materials (CA ...
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Use complex numbers in polynomial identities and equations. [Polynomials with real coefficients] N-CN 7. Solve quadratic equations with real coefficients that have complex solutions. N-CN 8. (+) Extend polynomial identities to the complex numbers. For example, rewrite x2 + 4 as (x + 2i)(x – 2i). N-CN 9.
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[DOC File]Quadratics
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E.1.a: Solve quadratic equations and inequalities using various techniques, including completing the square and using the quadratic formula. E.1.b: Use the discriminant to determine the number and type of roots for a given quadratic equation. E.1.c: Solve quadratic equations with complex number solutions.
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[DOC File]STANDARD
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The value of the discriminant of a quadratic equation can be used to describe the number of real and complex solutions. The definition of absolute value (for any real numbers a and b, where b 0, if , then a = b or a = - b) is used in solving absolute value equations and inequalities.
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[DOC File]Algebra I Standards Map - Instructional Materials (CA Dept ...
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Solve quadratic equations in one variable. 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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[DOC File]Module 2: The Quadratic Formula
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Since the radicand is negative in the example above, the solutions to the quadratic equation are complex numbers. The radicand in the quadratic formula is called the discriminant. DEFINITION: The . discriminant. of the quadratic equation is . example: The discriminant of the quadratic equation is . The discriminant tells us the nature of the ...
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[DOCX File]STANDARD
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Complex solutions occur in conjugate pairs. Quadratic equations with exactly one real root can be referred to as having one distinct root with a multiplicity of two. For instance, the quadratic equation, x 2 -4x+4 , has two identical factors, giving one real root with a multiplicity of two.
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[DOC File]Algebra II – Unit 1 – ELL Scaffold
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Writing Solve quadratic equations with real coefficients that have complex solutions. Describe and explain how to solve quadratic equations with real coefficients that have complex solutions using Manipulatives, word wall, Charts/Posters and Math Journal. VU: Function, equation, quadratic, real coefficients, solution LFC:
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[DOC File]Solving Quadratic Equations
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Equations such as x2 = 64, x2 -5x = 0, and x2 + 4x = 5 are called quadratic equations. This is because in each of these equations the greatest exponent of any variable is 2. Standard Form of Quadratic Equations: ax2 + bx + c = 0.
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[DOC File]Livingston County Schools
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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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[DOC File]Module 1: Solving Quadratic Equations
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In the next module we will study solving quadratic equations using the quadratic formula. SOLVING QUADRATIC EQUATIONS BY FACTORING. example: Solve the following quadratic equations by factoring. a. b. c. SOLUTIONS: Thus, the solution set is Thus, the solution set is . Thus, the solution set is . SOLVING QUADRATIC EQUATIONS USING THE SQUARE ROOT ...
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Complex solutions to quadratic equations