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.
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
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!
+128406 Set the y's equal and we get that
3x^2 + 4x - 5 = x^2 + 12 rearrange as
2x^2 + 4x - 17 = 0
Using the quad formula
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) )
