Question 1026786
Since the two graphs are supposed to intersect, let {{{(1/3)x^2 = x+c}}}

==> {{{x^2 = 3x + 3c}}} ==> {{{x^2 - 3x - 3c = 0}}}

For the two graphs to meet only at one point, the discriminant of the above quadratic equation has to be 0, or

{{{b^2 - 4ac = (-3)^2 - 4*1*(-3c) = 0}}}.

<==> 9 + 12c = 0

==> c = -9/12, or -3/4.