help pl 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

see below

Step-by-step explanation:

y=6x^2 +2x - 20

a=6  b= 2  c = -20

Quadratic Formula

-b ± sqrt( b^2 - 4ac)

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   2a

-2 ± sqrt( 2^2 - 4*6(-20))

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   2*6

-2 ± sqrt( 2^2 - 4*6(-20))

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

   2*6

-2 ± sqrt(484)

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   2*6

-2 ± 22

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   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

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

let x be the money she spent so that she can earn the free t-shirt.

since, she already spent $112.49

⇒

also, as per the statement: jennifer must spend $250 or more in order to qualify for a free t-shirt at the store.

then,

we have an inequality i.,e

subtract 112.49 from both sides we get;

therefore, $137. 51 more money does jennifer need to spend so that she can earn the free t-shirt