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Two parabolas are the graphs of the equations $y=2x^2-10x-10$ and $y=x^2-4x+6$.. Give all points where they intersect. List the points in order of increasing $x$-coordinate, separated by semicolons.

 Dec 30, 2018
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Equate the "y's"

 

2x^2 - 10x - 10 = x^2 - 4x + 6   rearrange as

 

x^2 - 6x - 16  =  0        factor

 

(x - 8) ( x + 2) =  0

 

Set both factors to 0 and solve for x  and we have that  x = -2  and x = 8

 

So....when x = - 2, y = (-2)^2 - 4(-2) + 6 =  18

 

And when x = 8, y =  (8)^2 -4(8) + 6 =  38

 

So

 

(-2, 18)   ;  (8, 38)

 

 

cool cool cool

 Dec 30, 2018

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