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The parabolas defined by the equations y = -x^2 - x + 1 and y = x^2 - 3x - 3 intersect at points (a,b) and (c,d), where c >= a. What is c - a? Express your answer as a common fraction.

 Jul 23, 2021
 #1
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-x^2   - x  + 1  =  x^2  - 3x  - 3        rearrange  as

 

2x^2 - 2x  - 4  =  0                divide through  by 2

 

x^2 - x  - 2  =  0                     factor as

 

( x - 2) ( x + 1)   = 0

 

Set  each factor to 0   and solve for x   and  we  get  that

 

x = 2  = c          and  x   =  -1   =  a

 

c - a   =

 

2 - (-1)   = 

 

3

 

 

 

cool cool cool

 Jul 23, 2021

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