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Two parabolas are the graphs of the equations y = 2x^2 - 7x - 1 and y = 8x^2 - 2x - 5. Give all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.

 Jun 14, 2021
 #1
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Set  the  equations  equal

 

2x^2  - 7x  - 1    =   8x^2  - 2x  -  5           rearrange as

 

6x^2  + 5x  -  4   =  0                    factor  as

 

(3x   + 4) ( 2x  - 1)   =  0

 

Set  each  factor to 0   and  solve for  x  and  the x intersection points  are

 

-4/3    and     1/2

 

When x  = -4/3   y =  2(-4/3)^2  - 7(-4/3)  - 1   = 107 / 9

 

When  x  =  1/2   y =   2 (1/2)^2  - 7(1/2)  - 1  =  -4

 

The points  are

 

(-4/3, 107/9)    and ( 1/2 ,  -4)

 

 

cool cool cool

 Jun 14, 2021

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