3 - Notes - Solving Quadratics With Imaginary
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
QUADRATICS UNIT Solving Quadratic Inequalities and Curve Fitting By graphing the inequality: y x2 – 7x 10, we can begin to look at what shading would look like: Looking at the inequality: y –3x2 – 6x – 7, write the solution: We can also use our knowledge of and and or to solve much faster: x2 12x 39 12 x2 – 24 5x or and
Unit 2-1 Factoring and Solving Quadratics Learning Targets: Factoring Quadratic Expressions 1. I can factor using GCF. 2. I can factor by grouping. 3. I can factor when a is one. 4. I can factor when a is not equal to one. 5. I can factor perfect square trinomials. 6. I can factor using difference of squares. Solving Quadratic Equations 7.
In total, we will use five strategies for solving quadratic equations: graphing, square rooting, factoring, completing the square, and using the Quadratic Formula. The last two sections extend work with solving quadratic equations to solving nonlinear systems and solving quadratic inequalities.
1 Solving Quadratics by Factoring (Day 10 . If necessary, express your answers in simplest radical form. 1. x2 2x 12 2. k(x) 2x2 8x 7 3. The perimeter of a triangle can be represented by the expression 5x2 10x 8. Write a polynomial that represents the measure of the third side. 16
Graphing-quadratics-worksheet-with-answers. SOLVING QUADRATIC EQUATIONS BY FACTORING WORKSHEET ANSWERS. SOLVING LINEAR. INEQUALITIES WORKSHEET KUTA POLYNOMIAL. Mar 19, 2021 — Worksheet Quadratic Equations solve Quadratic Equations by Peting from worksheet graphing quadratics from standard form answer . Aug 29, 2020 — Graphing quadratic
Nov 01, 2015 · Solving Quadratics by Factoring – Part 1 Solve a quadratic equation by factoring: Once a quadratic equation is factored, we can use the zero product property to solve the equation. ! The zero product property states that if the product of two factors is
The method described below utilizes two ideas: (1) When the product of two or more numbers is zero, then one of the numbers must be zero. (2) Some quadratics can be factored into the product of two binomials, where coefficients and constants are integers. This procedure is called the Zero Product Method or Solving by Factoring. See the
accounting equation as shown above. The accounting equation is a simple expression of the fact that at any point in time the assets of the entity will be equal to its liabilities plus its equity. The transactions of a new business entity in its first five days are as follows: Required:
