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If the parabola $y_1 = x^2 + 2x + 7$ and the line $y_2 = 6x + b$ intersect at only one point, what is the value of $b$?

 Jan 23, 2018
 #1
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y =   x^2 + 2x  + 7

y  =  6x  + b

 

Set these equal

 

x^2 + 2x  + 7   =  6x + b      rearrange as

 

x^2 -  4x  +  (7 - b)  = 0

 

If this only has one solution point....it must be that

 

(-4)^2  - 4(7 - b)   =  0

 

16  - 28  +  4b  = 0

 

-12   +  4b  =  0

 

-12   =  -4b       divide both sides by  -4

 

3  = b

 

This graph shows the intersection point of  (2, 15)

 

https://www.desmos.com/calculator/mlvins5guo

 

 

 

cool cool cool

 Jan 23, 2018

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