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Two parabolas are the graphs of the equations y=2x^2-10x-10 and y=x^2-4x-16. Find all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.

 Apr 23, 2022
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Set the two equations equal and solve.

 

2x^2-10x-10 = x^2-4x-16      step 1:  subtract x^2 from the both sides

-x^2                -x^2

 

x^2-10x-10 = -4x-16                step 2: add 4x to both sides

      +4x          +4x

 

x^2-6x-10 = -16                     step 3: add 16 to both sides

          +16    +16

 

x^2-6x+6 = 0                          step 4: use quadratic formula x = (-b +/- sqrt(b^2-4ac))/2a

 

x = (-(-6) +/- sqrt((-6)^2-4(1)(6)))/2(1)             step 5: plug in

 

x = (6 +/- 2*sqrt(3))/2                                      step 6: simplify 

 

x = 3 - sqrt(3); 3 + sqrt(3)                               answers

 Apr 23, 2022

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