created by mr. lafferty finding roots graphically finding roots by factorising finding roots using...

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created by Mr. Lafferty created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic Solving Quadratic www.mathsrevision.com Int 2

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Page 1: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Finding roots graphically

Finding roots by factorising

Finding roots using formula

Solving Quadratic Solving Quadratic w

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Int 2

Page 2: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

StarterStarter

2 2x +7x +6

Q3. Solve (2x -1)(x -1) = 0

1. Factorise the following.

2. A TV is reduced by 20% to £200.

What was the original price.

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Int 2

Page 3: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. Use graphs to locate Use graphs to locate roots of a quadratic roots of a quadratic equation.equation.

1. To sow how to solve quadratic equations graphically.

2.2. Solve quadratic Solve quadratic equations by finding the equations by finding the roots.roots.

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Int 2

Graphical Roots Graphical Roots

Page 4: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2Graphical Roots Graphical Roots

Finding the roots (solve) of a quadratic equation is simply finding where the graph crosses the x – axis ie. f(x) = 0

Example : Find the roots (solve) of the quadratic equations below.

3-2

f(x)

x 1-4

f(x)

x

Page 5: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Laffertyww

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Int 2Graphical Roots Graphical Roots

Page 6: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Laffertyww

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Int 2Graphical Roots Graphical Roots

Page 7: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Laffertyww

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Int 2Graphical Roots Graphical Roots

Page 8: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Now try MIA Ex 8Ch14 (page 228)

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Int 2Graphical Roots Graphical Roots

Page 9: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

(2,-2)

StarterStarterw

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Int 2

Q. Write down the function represented by the graphs below given that they are of the form and a is either 1 or -1.

(1,4)

f(x)

x (0,-2)(-2,-4)

f(x)

x

y = a(x - b)2 + c

Page 10: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To be able to factorise To be able to factorise quadratic equations.quadratic equations.

1. To explain how to find the roots (solve) quadratic equations by use of factorisation.

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Int 2

Roots Roots

Page 11: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2

When a number is multiplied by 0 the result is 0.

If 7b = 0 then b = 0

If ab = 0 then a = 0 or b = 0

If ( x-a )( x-b ) = 0 then either (x-a) = 0 or (x-b) = 0

Roots Roots

Note: The a,b in this form are NOT the a,b in the formf(x) ax2 + bx + c

Page 12: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2

Factorise 2x2-x-1 = 0

( 2x+1)(x-1) = 0

2x+1 = 0

x-1 = 0

x = -0.5

x = 1

or

either

Factorise y2+ 3y = 0

y(y + 3) = 0

y = 0

y = -3

or

either

y + 3 = 0

Examples Factorise using FOIL or St. Andrew’s Cross

Roots Roots

Page 13: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Find the roots of the quadratic equations.

Where it cut the x !!!!!!

Roots Roots

x2 + 7x + 10 = 0

x2 - 5x – 6 = 0 2x2 - 13x + 15 = 0

x2 + 6x + 8 = 0

x = 1.5, 5

x = -2, -5 x = -2, -4

x = 6, -1

(x – 6)(x + 1) = 0 (2x – 3)(x - 5) = 0

(x + 5)(x + 2) = 0 (x + 4)(x + 2) = 0

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Int 2

Page 14: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Now try MIA Ex9 (page 229)

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Int 2

Roots Roots

Page 15: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

StarterStarter

2

2

y = -(x +4) + 1

3. Try and f actorise x -3x +3

1. Sketch.

2. A shop owner wants to makes a 15%

profit on a cd's he buys for £8.

How much does he need to sell them for ?

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Int 2

Page 16: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Learning IntentionLearning Intention Success CriteriaSuccess Criteria

1.1. To be able to solve To be able to solve quadratic equations quadratic equations using quadratic formula.using quadratic formula.

1. To explain how to find the roots (solve) quadratic equations by use quadratic formula.

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Int 2

Factorise Roots Factorise Roots

Page 17: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2

When we cannot factorise or solve graphically quadratic equations we need to use the

quadratic formula.

Factorise Roots Factorise Roots

2-b ± (b -4ac)x =

2a

ax2 + bx + c

Page 18: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2

Example : Solve x2 + 3x - 3

Factorise Roots Factorise Roots

2-(3) ± ((3) -4(1)(-3))x =

2(1)

ax2 + bx + c

1 3 -3

-3 ± 21=

2

Page 19: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

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Int 2

Factorise Roots Factorise Roots

-3 + 21x =

2-3 - 21

x = 2

and

x = 0.8 x = -3.8

Page 20: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Use quadratic formula to solve the following :

Factorise Roots Factorise Roots

2x2 + 4x + 1 = 0

5x2 - 9x + 3 = 0 3x2 - 3x – 5 = 0

x2 + 3x – 2 = 0

x = 1.9, -0.9

x = -1.7, -0.3 x = -3.6, 0.6

x = 1.4, 0.4

Page 21: Created by Mr. Lafferty Finding roots graphically Finding roots by factorising Finding roots using formula Solving Quadratic  Int

created by Mr. Laffertycreated by Mr. Lafferty

Now try MIA Ex10 (page 232)

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Int 2

Factorise Roots Factorise Roots