Two graphs have a point of intersection if the equations of the graph have a solution. The equations of the graphs given are:

f(x)=2x+1 and g(x)=x^2+x+1

Equating the two we get 2x + 1 = x^2 + x + 1

=> x^2 - x = 0

=> x(x - 1) = 0

=> x = 1 and x = 0

y = 3 , 1

**The two graphs intersect at the point (1, 3) and (0, 1)**

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