![]() ![]() Lessons can start at any section of the PPT examples judged against the ability of the students in your class. Main: Lessons consist of examples with notes and instructions, following on to increasingly difficult exercises with problem solving tasks. Lesson 4.4.2h - Forming and solving quadratic equations (worded problems).Lesson 4.4.1h - Forming and solving quadratic equations (geometric problems).Lesson 4.3.2h - Completing the square - part 2 (a ≠ 1).Lesson 4.3.1h - Completing the square - part 1 (a = 1).Lesson 4.2.2h - The quadratic formula - part 2.A quadratic equation is one which must contain a term involving x2, e.g. Lesson 4.2.1h - The quadratic formula - part 1 Introduction This unit is about how to solve quadratic equations.Lesson 4.1.2h - Factorising harder quadratic equations (a ≠ 1).Lesson 4.1.1h - Factorising quadratic equations (a = 1).The worksheet could also be used independent of the PowerPoint lesson! These are designed to speed up the lesson (no copying down questions etc). At least one printable worksheets for students with examples for each lesson.Normal PowerPoint lessons with which you can use a clicker / mouse / keyboard to continue animations and show fully animated and worked solutions.Since the discriminant is 0, there is 1 real solution to the equation.A collection of EIGHT FULL LESSONS, which could definitely be extended to at least 10-11 lessons for the right classes, on solving quadratic equations by factorising, the quadratic formula or completing the square. Since the discriminant is negative, there are 2 complex solutions to the equation.Ī = 9, b = −6, c = 1 a = 9, b = −6, c = 1 Since the discriminant is positive, there are 2 real solutions to the equation.Ī = 5, b = 1, c = 4 a = 5, b = 1, c = 4 The equation is in standard form, identify a, b, and c.Ī = 3, b = 7, c = −9 a = 3, b = 7, c = −9 To determine the number of solutions of each quadratic equation, we will look at its discriminant. ![]() The left side is a perfect square, factor it.Īdd − b 2 a − b 2 a to both sides of the equation.ĭetermine the number of solutions to each quadratic equation. SOLVING QUADRATIC EQUATIONS In this brush-up exercise we will review three different ways to solve a quadratic equation. The solutions to a quadratic equation of the form ax2 + bx + c 0, where are given by the formula: To use the Quadratic Formula, we substitute the values of a, b, and c from the standard form into the expression on the right side of the formula. b a ) 2 and add it to both sides of the equation.Make the coefficient of x 2 x 2 equal to 1, by We start with the standard form of a quadratic equation and solve it for x by completing the square. Now we will go through the steps of completing the square using the general form of a quadratic equation to solve a quadratic equation for x. We have already seen how to solve a formula for a specific variable ‘in general’, so that we would do the algebraic steps only once, and then use the new formula to find the value of the specific variable. In this section we will derive and use a formula to find the solution of a quadratic equation. Mathematicians look for patterns when they do things over and over in order to make their work easier. By the end of the exercise set, you may have been wondering ‘isn’t there an easier way to do this?’ The answer is ‘yes’. If the quadratic side is factorable, factor, then set each factor equal to zero. FACTORING Set the equation equal to zero. When we solved quadratic equations in the last section by completing the square, we took the same steps every time. Methods for Solving Quadratic Equations Quadratics equations are of the form ax 2 bx c 0, where a 0 Quadratics may have two, one, or zero real solutions. Solve Quadratic Equations Using the Quadratic Formula techniques to solve a system of equations involving nonlinear equations, such as quadratic equations.
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