To find the y-intercept, or the point where a line crosses the x-axis, plug x=0 into the equation. The answer will be your y-intercept, because at the x-axis x=0.
f(x) = 2 x^2 - 12 x - 144
f(0)= 2(0^2)-12(0)-144
f(0)= 2(0)-0-144
f(0)= 0-144
f(0)= -144
Therefore, the y-intercept is (-144). Did that make sense? If not, comment with questions below.