Warm up – back of your books… A1: Think of TWO numbers that Multiply to make 6 Sum to make 5 B1: Think of TWO numbers that Multiply to make 5 Sum to make.

Slides:

Advertisements

Similar presentations

Factorising polynomials This PowerPoint presentation demonstrates two methods of factorising a polynomial when you know one factor (perhaps by using the.

Advertisements

Holt Algebra Factoring x 2 + bx + c Warm Up 1. Which pair of factors of 8 has a sum of 9? 2. Which pair of factors of 30 has a sum of –17? Multiply.

The Quadratic Formula..

WARM UP WHAT TO EXPECT FOR THE REST OF THE YEAR 4 May The Discriminant May 29 Chapter Review May 30 Review May 31 Chapter 9 Test June Adding.

6.5 – Solving Equations with Quadratic Techniques.

10.1 Graphing Quadratic Functions p. 17. Quadratic Functions Definition: a function described by an equation of the form f(x) = ax 2 + bx + c, where a.

Using the factoring method, what are the solutions of y = x 2 + 5x + 6.

Goal: Graph quadratic functions in the form y = ax 2 + bx + c.

Quadratics Solving equations Using “Completing the Square”

MA.912.A.4.2: Add, subtract, and multiply polynomials. Which of the following expressions is equivalent to (5x − 3) 2 ? A. 25x 2 − 30x + 9 B. 25x 2 −

Roots of Polynomials Quadratics If the roots of the quadratic equation are  and  then the factorised equation is : (x –  )(x –  ) = 0 (x –  )(x –

Graphing Quadratic Equations

Chapter 10.1 Notes: Graph y = ax 2 + c Goal: You will graph simple quadratic functions.

4.1 Graph Quadratic Functions in Standard Form

11.6 Solving Quadratic Systems. Two equations of the form Ax 2 + Bxy + Cy 2 + Dx + Ey + F = 0 considered together is called a quadratic system. You can.

4.9 – Graph and Solve Quadratic Inequalities A quadratic inequality in two variables can be written in one of the following forms: y < ax 2 + bx + c y.

Quadratic Equations Learning Outcomes  Factorise by use of difference of two squares  Factorise quadratic expressions  Solve quadratic equations by.

Solving Quadratic Equations Quadratic Equations: Think of other examples?

Quadratic Factorising If you can long multiply you can factorise!

9.1 – Graphing Quadratic Functions. Ex. 1 Use a table of values to graph the following functions. a. y = 2x 2 – 4x – 5.

Factoring – Day 4 Factoring Trinomials Objective: To factor trinomials whose quadratic coefficient is 1.

Warm Up 1.) What is the graph of the function y = -x 2 + 4x + 1?

WARM UP What is the x-coordinate of the vertex? 1.y = -2x 2 + 8x – 5 2.y = x 2 + 3x -2 4.

How does the value of a affect the graphs?

Factoring Quadratics Using the “X” method. Warm - up 1. (x - 7) 2 = x x (2k + 3) 2 = 4k k ( t - 6 )( t + 6 ) = t

Factoring Quadratic Trinomials a = 1 Chapter 10.5.

11/06/ Factorizing Quadratic Equations. 11/06/ x 2 ± bx ± c x 2 ± bx ± c If this is positive, both signs are the same. The numbers ADD to.

10-2 Graphing Quadratic Functions. Quadratic Functions (y = ax 2 +bx+c) When a is positive, When a is negative, When c is positive When c is negative.

Factoring Day 1 I can factor a quadratic expression. x 2 + 3x + 2 Rewrite as (x + 1)(x + 2)

Quadratic Graphs y = x 2 + 2x - 2 x x2x2 2x -2 y Remember that -2 in the equation is the intercept so it will run through

Algebra 1 Section 4.3 Graph Linear Equations by using Intercepts A linear equation (the graph is a line) takes the form Ax + By = C. Which are linear equations?

The Quadratic Formula..

How To Graph Quadratic Equations Standard Form.

Warm up Factor the expression.

Discriminant and Quadratic

The Quadratic Formula..

Curves Dr Duxbury.

Quadratic Inequalities

HW#8: Solving Quadratic Equations by Graphing: Baseball Path

Quadratic Formula Solving for X Solving for quadratic equations.

Factorising polynomials

Unit 7 Quadratics Graphing Quadratic Functions

Sum and Product of Roots

Warm up Using the distance formula, d = , to find the distance between the following sets of points: 1) (2, 5) and (-4, 7) 2)

Quadratic Graphs - Parabolas

9.2 Graphing Quadratic Functions

Quadratic Graphs y = x2 + 2x - 2

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

Find the x-coordinate of the vertex

REARRANGING FORMULAE 2.

Objective Solve quadratic equations by graphing.

Factorising quadratics

Adding and Subtracting Polynomials

Quadratic Graphs y = x2 + 2x - 2

WARM UP 3 EVALUATING RADICAL EXPRESSIONS Evaluate the radical expression when a = -1 and b = 5. (LESSON 9.1). b 2 − 11a b 2 +9a a 2 +8.

Solving Quadratic Inequations

Quadratic Graphs.

Graphing Quadratic Equations

The Quadratic Formula..

A, b and c can be any numbers

The Quadratic Formula..

A, b and c can be any numbers

Warm Up Find each product. 1. (x – 2)(2x + 7) 2. (3y + 4)(2y + 9)

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

Honors Algebra 2 Chapter 4

How To Graph Quadratic Equations.

A, b and c can be any numbers

Factorise and solve the following:

Presentation transcript:

Warm up – back of your books… A1: Think of TWO numbers that Multiply to make 6 Sum to make 5 B1: Think of TWO numbers that Multiply to make 5 Sum to make 6 C1: Think of TWO numbers that Multiply to make 12 Sum to make -7 A2: Think of TWO numbers that Multiply to make 12 Sum to make 4 B2: Think of TWO numbers that Multiply to make 11 Sum to make 12 C: Think of TWO numbers that Multiply to make 12 Sum to make -8 A3: Think of TWO numbers that Multiply to make 9 Sum to make 6 B3: Think of TWO numbers that Multiply to make -12 Sum to make 1 C: Think of TWO numbers that Multiply to make 12 Sum to make -13 A4: Think of TWO numbers that Multiply to make 18 Sum to make 9 B4: Think of TWO numbers that Multiply to make -6 Sum to make 1 C: Think of TWO numbers that Multiply to make 18 Sum to make -11

What we have learnt so far… we can plot a quadratic graph using a table of values y = x 2 + 5x + 6 y = x 2 + 5x + 4 y = x 2 + 7x + 10 y = x 2 + 8x + 12 x-2012 y x-2012 y x-2012 y x-2012 y

What we have learnt so far… we can plot a quadratic graph using a table of values y = x 2 + 5x + 6 y = x 2 + 5x + 4 y = x 2 + 7x + 10 y = x 2 + 8x + 12 x-2012 y x-2012 y x-2012 y x-2012 y

Factorisation – a recap a)4x + 12 b)6x - 20 c)ab + 2a d)x 2 - 6x e)8y y f)15xy - 25x

Simple Quadratics – ones you factorise normally 1.x 2 + 4x 2.x 2 -14x 3.x 2 + 3x 4.x 2 + x 5. 2x x 6. 3x x 7.5x x 8. 10x x

Quadratics – with three terms

Quadratics – with three terms

1.x 2 + 4x x x x 2 + 3x +2 4.x 2 + 5x x x x x x x x x + 16

Quadratics – with three terms

Quadratics – with three terms

Quadratics – with three terms

What we have learnt so far… we can plot a quadratic graph using a table of values y = x 2 + 5x + 6 y = x 2 + 5x + 4 y = x 2 + 7x + 10 y = x 2 + 8x + 12 x-2012 y x-2012 y x-2012 y x-2012 y