[tex]f(x)=x^2+12x+11\\[/tex]
Find the x-intercept, f(x) = 0
[tex]x^2+12x+11=0\\(x+11)(x+1)=0\\x=-11,-1[/tex]
There we get the x-intercepts, what about y-intercept? That's easy, (0,11). You don't even need to calculate to get the y-intercept as from
[tex]f(x)=ax^2+bx+c[/tex] (a=/0)
The y-intercept is "c" So if c = 2 then y-intercept is (0,2)
Or if you want to calculate for y-intercept.
then x=0
[tex]f(0)=0^2+12(0)+11\\f(0)=0+0+11\\f(0)=11[/tex]
There, we get the y-intercept which is (0,11).
Therefore, x-intercepts are (-11,0) and (-1,0)
y-intercept is (0,11)
and yeah, you kinda of got it right.