Do y=3x^2+5x+12 and y=3x-8 intercept with each other? If yes, at which point(s)?

This is like solving 2 simultaneous equations. Both equations are in a form of y=ax^2+bx+c. Equate both equations together and you got:
3x2+5x+12 = 3x-8

Put both polynomials at one side and you got:
3x2+2x+20 = 0

b2-4ac = 2- 4(3)(20) = -236 <0
Because b2 - 4ac <0, there are no real roots and the two equations do not intercept with each other.

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