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Quadratics Solving Quadratic Equations

Quadratics Solving Quadratic Equations. Solving by Factorising

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Page 1: Quadratics Solving Quadratic Equations. Solving by Factorising

Quadratics

Solving Quadratic Equations

Page 2: Quadratics Solving Quadratic Equations. Solving by Factorising

Solving by Factorising

equations. elementary theSolve :3 Step

.0or 0either

then,0 if :lawfactor null the Use:3 Step

side.other thefactoriseFully :2 Step

side. one to termsall ingby tranfer

zero toequalequation theof side one make :1 Step

rue.equation t themake which of valuesare

0cbx of solutionsor Roots:Definition 2

ba

ba

x

ax

Page 3: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 1

72

3 (e)

10116 (d)

414 (c)

65 (b)

053 (a)

:for x following theSolve

2

2

2

2

xx

xx

xx

xx

xx

Page 4: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 5: Quadratics Solving Quadratic Equations. Solving by Factorising

Solving by Completing the Square

for x. valuesthe

find andequation theundo toable then are We

square. the

completing of method theusingby

form in the 0 writeWe2

2

qpxa

cbxax

Page 6: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 2

073 (c)

75 (b)

3232 (a)

:for x Solve

2

2

2

x

x

x

Page 7: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 8: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 3

03102 (c)

043 (b)

014 (a)

:square thecompletingby following theSolve

2

2

2

xx

xx

xx

Page 9: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 10: Quadratics Solving Quadratic Equations. Solving by Factorising

Solving using the Quadratic Formula

a

acbbx

cbxax

2

4

:is 0 osolution t The

2

2

Page 11: Quadratics Solving Quadratic Equations. Solving by Factorising

Proof

Page 12: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 4

133-x

5x (d)

0432 (c)

022 (b)

0103 (a)

:formula quadratic theusing following theSolve

2

2

2

x

xx

xx

xx

Page 13: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 14: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 15: Quadratics Solving Quadratic Equations. Solving by Factorising

Approximate solution using Technology

• Draw the graph using the graphic calculator In y=

• Use an appropriate window• Find where the graph cuts the x-axis using 2nd

calc buttons

Page 16: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 5

1221x (c)

0143x (b)

0115 (a)

:osolution t eapproximat thefind y to technologUse

2

2

xx

x

xx

Page 17: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 18: Quadratics Solving Quadratic Equations. Solving by Factorising

Complex Roots

• Use the quadratic formula to solve• If the number under the square root is

negative treat it as an imaginary number and continu with the solution.

Page 19: Quadratics Solving Quadratic Equations. Solving by Factorising

Example 6

0134 (c)

0254x (b)

09 (a)

:for x Solve

2

2

2

xx

x

Page 20: Quadratics Solving Quadratic Equations. Solving by Factorising
Page 21: Quadratics Solving Quadratic Equations. Solving by Factorising

This Weeks Work

• Page 26 Ex 1E1 Q1 – 3• Page 28 Ex1E2 Q1 – 3• Page 31 Ex 1E3 Q1, 2• Page 12 Ex 1E4 Q1, 2• Page 33 Ex 1E5 Q1, 2