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A square is drawn such that one of its sides coincides with the line y = 7, and so that the endpoints of this side lie on the parabola y = 2x^2 + 6x + 4.  What is the area of the square?

 Jul 23, 2022
 #2
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We need to find  the width of the square........ we can   do  this as follows

 

2x^2 + 6x+ 4  = 7

 

2x^2 + 6x - 3  =  0

 

Using the q formula

 

 

x = [  -6 + sqrt ( 36 + 24) ]  / [ 2 *2] =    [ -6+ sqrt (60) ] / 4  =  [ -6  + 2sqrt (15) ]  / 4 =  sqrt (15)/2 -3/2

 

The other  root  is    -sqrt (15) / 2  - 3/2

 

These two points are where the parabola intersects the line y= 7

 

So....the width of the  square  =   (-3/2 + sqrt (15)/2)  - ( -3/2 - sqrt (15) / 2)  = 2 sqrt (15)  /2  = sqrt (15)

 

Area of the square =   (sqrt (15)) ^2  =    15

 

 

cool cool cool

 Jul 23, 2022

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