Question

help plzzzzzzzzzzzz not i am lost. 100 points or more if I can. Show how to solve the Quadratic Equation y=6x^2 +2x - 20 or a different equation you choose by ALL OF THE FOLLOWING METHODS: Using Quadratic Formula by hand Using Factoring and the Zero Property Product Using Completing the Square Using Graphing on the Calculator

Answer 1

Answer: and Step-by-step explanation:

y=6x² +2x - 20

let a=6

let b= 2

let c = -20

Using Quadratic Formula by hand Using Factoring and the Zero Property Product Using Completing the Square Using Graphing on the Calculator

using Quadratic Formula

-b ± √( b² - 4ac)

2a

-2 ± √( 2² - 4*6(-20))

2*6

-2 ± √( 2² - 4*6(-20))

2*6

-2 ± √(484)

2*6

20/12 = 5/3

-24/12 = -2

the answers are 5/3 ; -2

use by Factoring

0=6x² +2x - 20

0 =2( 3x² +x - 10)

=2 ( 3x-5) ( x+2)

by using the zero product property

3x-5 = 0

x+2 = 0

3x=5

x =-2

x = 5/3

x = -2

by using completing the square

y=6x² +2x - 20 Add 20

20=6x² +2x Divide by 6

20/6 = x² +2/6x

10/3 = x^2 +1/3x Take the coefficient of x and divide by 2

1/3 /2 = 1/6 Square it

(1/6) ² = 1/36 Add it to both side s

10/3 + 1/36 = x² +1/3x+ 1/36

120/36 + 1/36 = ( x+ 1/6)²

121/ 36= ( x+ 1/6)² Take the square root of both side

√(121/ 36) = √( ( x+ 1/6)²)

±11/6 = x+1/6 Subtract 1/6 from both side

-1/6 ±11/6 = x

-1/6 - 11/6 = x

-1/6 + 11/6 = x

-12/6 =x

10/6 =x

x = -2

x = 5/3

by using a graphing computer

Answer 2

see below

Explanation:

y=6x^2 +2x - 20

a=6 b= 2 c = -20

Quadratic Formula

-b ± sqrt( b^2 - 4ac)

------------------------------

2a

-2 ± sqrt( 2^2 - 4*6(-20))

------------------------------

2*6

-2 ± sqrt( 2^2 - 4*6(-20))

------------------------------

2*6

-2 ± sqrt(484)

------------------------------

2*6

-2 ± 22

------------------------------

12

20/12 = 5/3 -24/12 = -2

solutions are 5/3 and -2

Factoring

0=6x^2 +2x - 20

0 =2( 3x^2 +x - 10)

=2 ( 3x-5) ( x+2)

Using the zero product property

3x-5 = 0 x+2 = 0

3x=5 x =-2

x = 5/3 x = -2

Completing the square

y=6x^2 +2x - 20

Add 20

20=6x^2 +2x

Divide by 6

20/6 = x^2 +2/6x

10/3 = x^2 +1/3x

Take the coefficient of x and divide by 2

1/3 /2 = 1/6

Square it

(1/6) ^2 = 1/36

Add it to each side

10/3 + 1/36 = x^2 +1/3x+ 1/36

120/36 + 1/36 = ( x+ 1/6) ^2

121/ 36= ( x+ 1/6) ^2

Take the square root of each side

sqrt(121/ 36) = sqrt( ( x+ 1/6) ^2)

±11/6 = x+1/6

Subtract 1/6 from each side

-1/6 ±11/6 = x

-1/6 - 11/6 = x -1/6 + 11/6 = x

-12/6 =x 10/6 =x

-2 =x 5/3 =x

Graphing