Starter To make sure that you can re-arrange equations

Slides:

Advertisements

Similar presentations

solution If a quadratic equation is in the form ax 2 + c = 0, no bx term, then it is easier to solve the equation by finding the square roots. Solve.

Advertisements

Day 5 Simplify each expression: Solving Quadratic Equations I can solve quadratic equations by graphing. I can solve quadratic equations by using.

Many quadratic equations can not be solved by factoring. Other techniques are required to solve them. 7.1 – Completing the Square x 2 = 20 5x =

7.1 – Completing the Square

Solving quadratic equations Factorisation Type 1: No constant term Solve x 2 – 6x = 0 x (x – 6) = 0 x = 0 or x – 6 = 0 Solutions: x = 0 or x = 6 Graph.

Section 8.1 Completing the Square. Factoring Before today the only way we had for solving quadratics was to factor. x 2 - 2x - 15 = 0 (x + 3)(x - 5) =

E Maths Lecture Chapter 1: Solutions of Quadratic Equations.

Fireworks – Finding Intercepts

Module :MA0001NP Foundation Mathematics Lecture Week 9

Whiteboardmaths.com © 2008 All rights reserved

Solving Quadratic Equations by Factoring. Solution by factoring Example 1 Find the roots of each quadratic by factoring. factoring a) x² − 3x + 2 b) x².

Pre calculus Problem of the Day Homework: p eoo, odds Factor the following:

Warm-ups Find each product. 1. (x + 2)(x + 7)2. (x – 11)(x + 5) 3. (x – 10) 2 Factor each polynomial. 4. x x x 2 + 2x – x 2.

Introduction to Quadratic Equations & Solving by Finding Square Roots Chapter 5.3.

Calculus 3.4 Manipulate real and complex numbers and solve equations AS

2.6 Solving Quadratic Equations with Complex Roots 11/9/2012.

Learning Task/Big Idea: Students will learn how to find roots(x-intercepts) of a quadratic function and use the roots to graph the parabola.

1. 2. * Often times we are not able to a quadratic equation in order to solve it. When this is the case, we have two other methods: completing the square.

Derivation of the Quadratic Formula The following shows how the method of Completing the Square can be used to derive the Quadratic Formula. Start with.

Whiteboardmaths.com © 2008 All rights reserved

Solving Equations Using Factoring

The Quadratic Formula Students will be able to solve quadratic equations by using the quadratic formula.

Solve by factoring. x² = - 4 – 5x 2,. Solve by factoring. n² = -30 – 11n -4 and -1.

Quadratic Formula. Solve x 2 + 3x – 4 = 0 This quadratic happens to factor: x 2 + 3x – 4 = (x + 4)(x – 1) = 0 This quadratic happens to factor: x 2.

Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.

Deriving the Quadratic Formula. The Quadratic Formula The solutions of a quadratic equation written in Standard Form, ax 2 + bx + c = 0, can be found.

Difference between Expression and Equation?. L.O. To be able to solve Quadratic Equations There are several ways to solve a quadratic equation Factorising.

CHAPTER 10 LESSON OBJECTIVES. Objectives 10.1 Students will be able to: Identify quadratic functions and determine whether they have a minimum or maximum.

Martin-Gay, Developmental Mathematics 1 Warm-Up #28 (Thursday, 11/12)

Bellwork Use the distributive property to find each product. 1. (x+2)(x -5) 2. (-3x+2)(2x-6) Identify whether each function is quadratic. 3. f(x) = 4x³.

Ch 10: Polynomials G) Completing the Square Objective: To solve quadratic equations by completing the square.

Algebra 3 Lesson 2.6 Objective: SSBAT solve quadratic equations. Standards: M11.D

Q. A quadratic equation is An equation with 1 solution An equation with 2 solutions An equation with 0 solutions An equation with 3 solutions.

Algebra Completing the Square. Solving with Square Roots.

10.6B Best Method. Standard Form: Square Root Method: 1. When b = 0 2. Get x 2 alone 3. Square root both sides 4. plus/minus answer.

Topic 5 Modeling with Linear and Quadratic Functions 5.7 The Quadratic Formula and the Discriminant.

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

The Quadratic Formula Quadratic Formula.

The Quadratic Formula..

Deriving the Quadratic Formula

5.6 Quadratic Formula & Discriminant

The Quadratic Formula..

Quadratic Formula Solving for X Solving for quadratic equations.

Solving Quadratic Equations

Solving Quadratic Equations by the Complete the Square Method

What is an equation? An equation is the equality of two different expressions. This equality is true only for a number of dinstinct values (or none) of.

Quadratic Equations.

Solve a quadratic equation

Solving quadratic equations

DCA Answers 1. C 2. G 3. B 4. F 5. D 6. F 7. B 8. F 9. B 10. H 11. D

Algebra 1 Section 12.5.

I CAN solve equations using the Quadratic Formula. lesson 9.4a.

Solving Equations Using Factoring

10.7 Solving Quadratic Equations by Completing the Square

Quadratic Equations.

9.2 Solving Quadratic Equations using square roots

Chapter 10 Final Exam Review

Solving the Quadratic Equation by Completing the Square

3.4 – The Quadratic Formula

3.5 Solving Nonlinear Systems

The Quadratic Formula..

Starter Multiply out the brackets: (x+3)(x+3) (x+2)2 (x-5)2 Factorise:

The Quadratic Formula..

quadratic formula. If ax2 + bx + c = 0 then

Difference between Expression and Equation?

Equations Involving Absolute Value

Presentation transcript:

Starter To make sure that you can re-arrange equations Make “x” the subject of the formula v = ω√(a² -x²) so x= ? 5 November, 2019 INTO - Foundation L4/5 MH

Lesson 4-5 Quadratic equations Objectives - To solve quadratic equations by factorisation - To solve quatratic equations by completing the square - To solve quadratic equations by formula 5 November, 2019 INTO - Foundation L4/5 MH

Quadratic equations These occur naturally e.g. The length of a rectangular field is 40m greater than its width. Its area is 6000m2 Form an equation to find the length of the field 5 November, 2019 INTO - Foundation L4/5 MH

Quadratic equations Usually have two solutions Look like parabolas Take the form Do you know how a,b,c effect the quadratic curve ? 5 November, 2019 INTO - Foundation L4/5 MH

They look something like this 5 November, 2019 INTO - Foundation L4/5 MH

Factorising quadratics Factorise X2+7x+12 ( x + ) ( x+ ) X2-2x-24 ( x+ ) (x- ) 12X2-17x-7 factors of 12 (4,3), (6,2),(12,1) factors of 7 (7,1) ( x+ ) ( x- ) 5 November, 2019 INTO - Foundation L4/5 MH

Solving quadratics Once we have factorised the quadratic we have the solution X2+5x+6 = 0 (x+2)(x+3)=0 so x=-2 and x=-3 These are also known as the roots of the equation Obviously, not all quadratics factorise !! 5 November, 2019 INTO - Foundation L4/5 MH

Can’t factorise it Then we complete the square OR We use the quadratic formula Completing the square implies that the form of Is written as 5 November, 2019 INTO - Foundation L4/5 MH

Complete the square and solve 8x2 + 64x – 40 Step 1 divide by a Step 2 write Step 3 subtract the squared term 5 November, 2019 INTO - Foundation L4/5 MH

To solve Rearrange the equation Take the square roots of both sides Rearrange for x 5 November, 2019 INTO - Foundation L4/5 MH

Derive the Quadratic formula 5 November, 2019 INTO - Foundation L4/5 MH

Derive quadratic formula 5 November, 2019 INTO - Foundation L4/5 MH

Worksheet I have a worksheet to hand out Factorise the first sets of equations Complete the square to solve the second set of equations Use the quadratic formula to solve the last set of equations 5 November, 2019 INTO - Foundation L4/5 MH