SOLUTION: What is the maximum value of c such that the graph of the parabola y = 1/3*x^2 has at most one point of intersection with the line y = x+c?

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: What is the maximum value of c such that the graph of the parabola y = 1/3*x^2 has at most one point of intersection with the line y = x+c?       Log On


   

Question 1026786: What is the maximum value of c such that the graph of the parabola y = 1/3*x^2 has at most one point of intersection with the line y = x+c?
Answer by robertb(5830) About Me  (Show Source):
You can put this solution on YOUR website!
Since the two graphs are supposed to intersect, let %281%2F3%29x%5E2+=+x%2Bc
==> x%5E2+=+3x+%2B+3c ==> x%5E2+-+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%5E2+-+4ac+=+%28-3%29%5E2+-+4%2A1%2A%28-3c%29+=+0.
<==> 9 + 12c = 0
==> c = -9/12, or -3/4.