college algebra
posted by mary .
, for this problem f(x)=3x^26x7,what is the minimum value and where do it occurs, and what is this functions domain and range?

for any parabola, the min/max occurs where x = b/2a
In your case, at x=6/6 = 1
domain for any polynomial is all reals
f(x) = 3x^2  6x  7
= 3(x1)^2  10
from this you can easily see that the min at x=1 is 10
so the range is all reals >= 10 
By completing square,
f(x) = 3[x^2 2x  7/3]
= 3[x^2  2(x)(1) + (1)^2  (1)^1  7/3]
= 3[(x  1)^2  1  7/3]
= 3(x  1)^2  3  7
= 3(x  1)^2  10