Camilla, Alice and Helena

Slides:

Advertisements

Similar presentations

Starter Revision Worksheet. Note 6: Expanding Brackets One Bracket: Multiply the outside term by everything inside the brackets Simplify if possible Examples:

Advertisements

Means writing the unknown terms of a quadratic in a square bracket Completing the square Example 1 This way of writing it is very useful when trying to.

Quadratic Equations A quadratic is any expression of the form ax 2 + bx + c, a ≠ 0. You have already multiplied out pairs of brackets and factorised quadratic.

Chapter 4 Quadratics 4.6 Completing the Square to Determine Max or Min Algebraically.

2.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Rationalise Surds.

+ Completing the Square. + In your notes: Simplify the following: (5 – 3i)(4 + 2i) 3.

9.4 – Solving Quadratic Equations By Completing The Square

E Maths Lecture Chapter 1: Solutions of Quadratic Equations.

6-4 Completing the Square Objective: Students will be able to solve quadratic equations by completing the square.

Linear Equations Learning Outcomes

Warmup 9-11 Solve the following equations by factoring. Show work! 1.x x - 80 = 0 2.Solve by using the quadratic formula: 4x 2 - 5x - 2 = 0 3.Solve.

Converting Quadratic Equations A step-by-step guide with practice.

Removing Common Factors Difference of Two Squares Factoring: Puzzle Method Perfect Square Trinomials Sum or Difference of Two Cubes ( )( ) = 0 u 2 = constant.

Use the Distributive Property to: 1) simplify expressions 2) Solve equations.

Solving Quadratic Equations – Part 1 Methods for solving quadratic equations : 1. Taking the square root of both sides ( simple equations ) 2. Factoring.

For a quadratic function, how to find the coordinates of the vertex of its graph? 2. Functions and Graphs (a) For y = a(x - h) 2 +k, the vertex of the.

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.

Factoring Polynomials by Completing the Square. Perfect Square Trinomials l Examples l x 2 + 6x + 9 l x x + 25 l x x + 36.

Solving Quadratic Equations – Quadratic Formula The following shows how to solve quadratic equations using the Quadratic Formula. A quadratic equation.

5.3 Solving Quadratic Functions with Square Roots Step 1: Add or subtract constant to both sides. Step 2: Divide or multiply coefficient of “x” to both.

Quadratics Day 2! VERTEX FORM Unit 6 Quadratic Functions Math II.

The area of the rectangle is the sum of the areas of the algebra tiles. The area of each square green tile is x² square units. The area of each long green.

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

Brackets An introduction to using brackets in algebra.

Parabola Formulas Summary of Day One Findings Horizonal Parabolas (Type 2: Right and Left) Vertical Parabolas (Type 1: Up and Down) Vertex Form Vertex:

Expanding Brackets Multiply the contents of the bracket by what is immediately outside it E.g. 3(a+4) 3a3a x a + 3 x 4.

Solving Quadratics Algebra 2 Chapter 3 Algebra 2 Chapter 3.

MTH 091 Sections 3.1 and 9.2 Simplifying Algebraic Expressions.

1.2 Quadratic Equations. Quadratic Equation A quadratic equation is an equation equivalent to one of the form ax² + bx + c = 0 where a, b, and c are real.

SOLVING QUADRATIC EQUATIONS BY COMPLETING THE SQUARE

The Quadratic Formula Quadratic Formula.

Simultaneous Equations 1

Grade 10 Academic (MPM2D) Unit 4: Quadratic Relations Quadratic Formula Mr. Choi © 2017 E. Choi – MPM2D - All Rights Reserved.

Solving Quadratic Equations by Completing the Square

Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

Distributive Property with Equations

Solving Quadratic Equations by the Complete the Square Method

Math 2 Fall Semester Final Review.

Section 3.5: Convert Standard to Vertex Form

Section 11.2 The Quadratic Formula.

Substitute numbers into expressions Find and use formulae

Changing the subject of the formula

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

Class Notes 11.2 The Quadratic Formula.

The Quadratic Formula.

Quadratic Equations by Dr. Terri

Brackets, Factors and Equations

9.4 Solving Quadratic Equations

Changing the subject of the formula

Maths Unit 14 – Expand, factorise and change the subject of a formula

Algebra and Functions.

Quadratics Multiply out (x+16) (x-16) (x+12) (x-12) = ?

Solving Quadratic Equations by Completing the Square

5.4 Completing the Square Objective: To complete a square for a quadratic equation and solve by completing the square.

10. Solving Equations Review

10. Solving Equations Review

Unit 23 Algebraic Manipulation

Completing the Square.

LINEAR EQUATIONS.

Warm Up Solve for x. Simplify Simplify

LINEAR EQUATIONS.

Solving Equations Review

Further Investigating Quadratics

L5-7 Objective: Students will be able to solve quadratics by using the quadratic formula.

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

Expanding Brackets: Single brackets with

Complete the Square January 16, 2017.

Maths Unit 15 – Expand, factorise and change the subject of a formula

Solving Linear Equations

Presentation transcript:

Camilla, Alice and Helena QUADRATICS Camilla, Alice and Helena

QUADRATIC EQUATION

STANDARD FORM What is it? Formula the standard form of a quadratic function can be used to solve any quadratic equation 𝑎𝑥 2 +𝑏𝑥+𝑐=0 a, b, c are known values x is the unknown variable e.g. 2𝑥 2 +5𝑥+3=0 a = 2 b = 5 c = 3 a b c

FACTORIZING

FACTORIZING QUADRATICS find the two factors of a standard form equation e.g. (x + 4) and (x - 1) are the two factors of x2 + 3x – 4 = 0

EXERCISES 2 x 2 +4x+4=0 x 2 +3x+15=0 3 x 2 +5x+25=0 Ext. 𝑥 2 +13𝑥=30

COMPLETING THE SQUARE What is it? Steps is a method of solving quadratic equation take the standard form for the quadratic equation: 𝑎𝑥 2 +𝑏𝑥+𝑐=0 and turn it into this: 𝑎(𝑥+𝑑) 2 +𝑒=0 half the coefficient of 𝑥 Simplify Solve 𝑥 2 +10𝑥+10=0 (𝑥+5) 2 − (5) 2 +10=0 𝑥+5 2 −25+10=0 𝑥+5 2 −15=0 𝑥+5 2 =15 𝑥+5=± 15 𝑥 =−5± 15 completed square form just solving vertex: 𝑥+5 2 −15=0 −5 ;−15

EXERCISES 2 x 2 +4x+4=0 x 2 +3x+15=0 3 x 2 +5x+25=0 Ext. 𝑥 2 +13𝑥=30

expanding pairs of brackets EXPANDING BRACKETS To remove (expand) brackets, we need to multiply the term on the outside of the bracket with each term inside the brackets. This process is also known as the distributive law. expanding pairs of brackets The first step is to multiply the first terms from each of the bracket, the 1st term in the 1st bracket with the 1st term in the 2nd bracket Then you need to multiply the two outside terms ,the 1st term in the 1st bracket with the 2nd term in the 2nd bracket, then multiply the two inside terms. The last step is to then multiply the last terms from each of the brackets .

EXERCISES