Slideshow 16, Mathematics Mr Richard Sasaki, Room 307.

Slides:

Advertisements

Similar presentations

Start with your equation Move the # term to the other side, and leave a space Determine what HALF of the coefficient of X is Factor the left side Write.

Advertisements

Completing the square This is an important algebraic technique that has important applications in the study of the properties of parabolic graphs. There.

SOLVING QUADRATICS General Form: Where a, b and c are constants.

Solving Quadratic Equations Using Square Roots & Completing the Square

Slideshow 13, Mathematics Mr Richard Sasaki, Room 307.

Expanding Brackets with Surds and Fractions

Solving Quadratic Equations by Factorisation Slideshow 19 Mathematics Mr Sasaki Room 307.

Solving Quadratic Equations by Completing the Square.

Slideshow 4 Mr Richard Sasaki Room 307 Multiplying Polynomials by a Number.

Slideshow 10, Mathematics Mr Richard Sasaki, Room 307 Powers and Indices.

Simplifying Surds Slideshow 6, Mr Richard Sasaki, Room 307.

USING THE FORMULA (SOLVING QUADRATICS) Slideshow 18, Mathematics Mr Richard Sasaki, Room 307.

Solve to find the zeros of y = -0.8x Replace y = 0 Eliminate the constant c by undoing + 84 Divide by the coefficient A on both sides. Undo -0.8.

Square Rooting Equations Slideshow 19, Mathematics, Mr Richard Sasaki, Room 307.

{ Solving Equations Slideshow 9, Mathematics Room 307, Mr Richard Sasaki.

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.

Warm Up  Find the roots. Solving Quadratic Equations by Completing the Square.

Calculating Square Roots – Part 2 Slideshow 4, Mr Richard Sasaki, Room 307.

Solving by Completing the Square What value would c have to be to make the following a perfect square trinomial?

Equations with Decimal and Fractional Terms Slideshow 22, Mathematics Mr Richard Sasaki Room 307.

An Introduction to Equations Slideshow 17, Mathematics Mr Richard Sasaki Room 307.

Applications of Quadratic Equations Slideshow 23, Mathematics Mr Richard Sasaki, Room 307.

Equations with Numbers and Unknowns on Both Sides Slideshow 21, Mathematics Mr Richard Sasaki Room 307.

Drawing Quadratic Curves – Part 2 Slideshow 28, Mathematics Mr. Richard Sasaki, Room 307.

Slideshow 1, Mathematics Mr Richard Sasaki Room 307 Room 307 Collecting Like Terms.

Aim: How do we solve quadratic equations by completing square?

Slideshow 22, Mathematics Mr Richard Sasaki, Room 307

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

The Square Root Principle & Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Completing the Square 8

Derivation of the Quadratic Formula

Aim: How do we solve quadratic equations by completing square?

4.6 Completing the Square Learning goals

4.6 Completing the Square Learning goals

Solving Quadratic Equations by Completing the Square

Squarely brought to you squares by

Algebra II Section 4.5a Complete the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Adding and Subtracting Polynomials – Part 2

Solving Quadratic Equations by Completing the Square

Expanding brackets and substitution

Drawing Quadratic Curves – Part 2

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Calculating Square Roots – Part 2

Completing the Square MM3G2.

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Surd Bracket Expansion

Solving Quadratic Equations by Completing the Square

4.5: Completing the square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Factorisation

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

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

Expanding Brackets with Surds and Fractions

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Solving Quadratic Equations by Completing the Square

Presentation transcript:

Slideshow 16, Mathematics Mr Richard Sasaki, Room 307

 Objectives

 Solving through factorisation Example

 Completing the Square

 Example Completing the Square It makes it easier if we move the constant to the other side. We need ( x + 3) 2 = a. (Note 3 is half of 6 as this would produce 3x + 3x. To get ( x + 3) 2 we half 6 and then square it. 3 9 Now write the left as ( x + a) 2. Square root both sides and solve!

 Completing the Square There is a lot to remember! Example Halve and square. 16 = 2 or -10 You must show your working!

 Completing the Square

 When completing the square it is easy to make a small mistake, be careful! When we have a negative coefficient of x, the symbol within the squared brackets will also be negative. Make sure you carry the negative symbol!

 Negative Cases Example The addition to each side is always positive as (½ x ) 2 > 0.

 Completing the Square