How many times does the function intersect the x axis?

Question

A teacher writes the function  on the board. How many times does the graph of the teacher’s function intersect the -axis?

Answer 1

3x^2 -18 +27 =0 has a discriminant = b^2 -4ac = 18^2 -4(3)(27) =0

when b2-4ac =0 there is no intersection, but the graph does touch the x-axis and there are 2 roots or zeroes which repeat. The graph just touches or is tangent to the x-axis. at x =-b/2a = 18/6 = 3

if you did the full quadratic formula, x = 3 + 0 or x=3+0 and 3-0, so the 3 "repeats"