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3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Quadratic FunctionsMGSE9 12.N.CN.7 Solve quadratic equations with real coefficients thathave complex solutions by (but not limited to) square roots, completingthe square, and the quadratic formula.MGSE9 12.A.REI.4 Solve quadratic equations in one variable.MGSE9 12.A.REI.4b Solve quadratic equations by inspection (e.g., forx2 49), taking square roots, factoring, completing the square, and thequadratic formula, as appropriate to the initial form of the equation (limitto real number solutions).Jan 4 9:06 AMWhat am I learning today?The methods to solve quadratic functionsHow will I show that I learned it?Solve a quadratic using any method and write theanswer in the correct format.Jan 4 9:34 AM1

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Forms of Quadratics1. Standard Form: f(x) ax2 bx c2. Vertex Form:f(x) a(x h)2 k3. Factored Form: f(x) a(x r1)(x r2)Jan 19 10:23 PMStandard form of a Quadraticax2 bx c 0Discriminant: b2 4acDiscriminant 0: 2 real rootsDiscriminant 0: 1 real rootDiscriminant 0: 2 imaginary rootsJan 19 10:23 PM2

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratica. Factoring (only rational answers)b. Taking a Square Rootc. Quadratic Formulad. Completing the SquareJan 19 9:47 PMSolving a Quadratic by FactoringExample 1: 6x2 2xJan 19 9:49 PM3

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratic by Square RootExample 1:3(x 6)2 7 43Jan 19 9:47 PMSolving by Quadratic Formula1. Put in standard form and set equal to 0.2. Label a, b, and c.3. Plug into the formula and simplify.Jan 19 10:11 PM4

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving by Quadratic FormulaExample 1: 6x2 2x 12 2x2 2x 3Jan 19 10:11 PMSolving by Quadratic FormulaExample 2: 2x2 4x 11 x2 2xJan 19 10:11 PM5

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratic by Completing the Square1. Move the x2 and x terms to one side.2. Move the constant to the opposite side.3. Divide by a.4. Addto each side of the equation to make aperfect square trinomial.5. Factor the perfect square.6. Solve by square roots.Jan 19 9:49 PMSolving a Quadratic by Completing the SquareExample 1:2x2 8x 8 4Jan 19 10:05 PM6

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratic by Completing the SquareExample 2:6x2 3 11xJan 19 10:05 PMSolving a Quadratic Inequality1. Turn into an equation and solve using any method.2. Plot solutions on a numberline paying attention towhether the points are part of the solution. Pick a pointin between the answers to test in the original inequality.3. If the point makes the inequality true, the solutionsare between the roots. If false, the solutions are outsideof the roots.4. Shade the solution set and write the solution set ininterval notation.Jan 19 9:49 PM7

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratic InequalityExample 1:2x2 2x 15 15xJan 19 9:49 PMSolving a Quadratic InequalityExample 2:2(x 3)2 8Jan 19 9:49 PM8

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017Solving a Quadratic InequalityExample 3:3x2 12 2x2 6xJan 19 9:49 PMPracticeSolve by Factoring:1. 2x2 6x x2 272.5x3 6x2 9x2 10xJan 19 9:49 PM9

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017PracticeSolve by Quadratic Formula:1. x2 8x 162. 6x2 9x2 10Jan 19 9:49 PMPracticeSolve by Completing the Square:1. x2 6x 162. 6x2 9x2 10Jan 19 9:49 PM10

3 Notes Solving Quadratics with Imaginary Numbers.notebookJanuary 11, 2017PracticeSolve the Inequality.1. x2 2x 2x 442. (x 3)2 12Jan 19 9:49 PMPracticeGraph the Quadratic and Find all its Characteristics.f(x) 2(x 2)2 7Vertex:AoS:Domain:Range:Extrema:Root(s):Y Int:Int. of Inc:Int of Dec:End Behavior:Jan 19 9:49 PM11

3 Notes Solving Quadratics with Imaginary Numbers.notebook 1 January 11, 2017 Jan 4 9:06 AM Quadratic Functions MGSE9 12.N.CN.7 Solve quadratic equations with real coefficients that have complex solutions by (but not limited to) square

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