Question 1089045
using the Completing square method:

f(x) = (x^2-6x+c) = ((x-3)^2 -3^2 + c = (x-3)^2 +(c-9).

in order to have only one intercept: (c-9) = 0, so c=9.

in this case: the intercept on the x-axis is when x = 3

@natolino_