the quadratic formula. what does the quadratic formula do ? the quadratic formula allows you to find...

6
The Quadratic Formula a ac b b x 2 4 2

Upload: grant-leonard

Post on 02-Jan-2016

219 views

Category:

Documents


3 download

TRANSCRIPT

Page 1: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

The Quadratic Formula

a

acbbx

2

42

Page 2: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

What does the Quadratic Formula Do ?

The Quadratic formula allows you to find the roots of a quadratic equation (if they exist) even if the quadratic equation does not factorize.

The formula states that for a quadratic equation of the

form : ax2 + bx + c = 0

The roots of the quadratic equation are given by :

a

acbbx

2

42

Page 3: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Example 1

Use the quadratic formula to solve the equation : x 2 + 5x + 6= 0

Solution:

Given: x 2 + 5x + 6= 0

Where a = 1 b = 5 c = 6

a

acbbx

2

42

12

)614(55 2

x

2

)24(255 x

2

15x

2

15

2

15

xorx

x = - 2 or x = - 3

These are the roots of the original equation.

and

then, substituting gives

Page 4: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Example 2

Use the quadratic formula to solve the equation: 8x 2 + 2x - 3= 0

Solution:

Given: 8x 2 + 2x - 3= 0

Where a = 8 b = 2 c = -3

a

acbbx

2

42

82

)384(22 2

x

16

)96(42 x

16

1002x

16

102

16

102

xorx

x = ½ or x = - ¾

These are the roots of the original equation..

and

then, substituting gives

Page 5: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Example 3

Use the quadratic formula to solve the equation: 8x 2 - 22x + 15= 0

Solution:

Given: 8x 2 - 22x + 15= 0

Where a = 8 b = -22 c = 15

a

acbbx

2

42

82

)1584()22()22( 2

x

16

)480(484(22 x

16

422x

16

222

16

222

xorx

x = 3/2 or x = 5/4 These are the roots of the original

equation.

and

then, substituting gives

Page 6: The Quadratic Formula. What does the Quadratic Formula Do ? The Quadratic formula allows you to find the roots of a quadratic equation (if they exist)

Example 4

Use the quadratic formula to solve for x to 2 decimal places: 2x 2 +3x - 7= 0

Solution:

Given: 2x 2 + 3x – 7 = 0

Where a = 2 b = 3 c = - 7

a

acbbx

2

42

22

)724(33 2

x

4

)56(93 x

4

653x

4

06.83

4

06.83

xorx

x = 1.27 or x = - 2.77These are the roots of the original

equation.

and

then, substituting gives