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# alg 1 question

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Two parabolas are the graphs of the equations y = 3x^2 + 4x - 5  and y = x^2 + 12. Give all points where they intersect. List the points in order of increasing x-coordinate, separated by semicolons.

Dec 3, 2020

#1
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It is solved here by the almighty hecticar, if not understood me and Cphill will give a thorough explanation https://web2.0calc.com/questions/help_50197

Dec 3, 2020
#2
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And btw Cphill I have a question below called "Cphill this ones for you"! Check it out if you can, if not I'll just try to solve it again since I have tried to solve it before. thx in advance!

Dec 3, 2020
#3
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Set the y's  equal  and we  get that

3x^2  +  4x   - 5 =   x^2  +  12       rearrange as

2x^2  +  4x  -  17  =   0

Lesser  x  =     [  -4  - sqrt [  4^2  - 4(2)(-17) ]   ]  /  (2*2)  =    ( -4 - sqrt [ 152 ]) / 4  =  ( -4 - 2sqrt (38) )  /4  =

-1  - sqrt (38)/2

Greater x  =  the conjugate =   -1  + sqrt (38)/2

y = (  1 + sqrt (38) / 2) )^2  +  12  =   ( 1  + sqrt (38)  +  38/4)  + 12  = (1 + 19/2  + 12 ) + sqrt (38)  =

45/2  + sqrt (38)

y =  (sqrt (38/2 - 1)) ^2  +  12   =  (38/4  - sqrt (38)  + 1) + 12  =  45/2 - sqrt (38)

Solutions

(-1 -sqrt (38)/2  , 45/2 + sqrt (38) )  ;    ( -1 + sqrt (38)/2 , 45/2 - sqrt (38)  )   Dec 3, 2020