Question 159977
You are being asked to use trial and error to grind out the answer.
Let's do 1, then you can do the others

 y=3x^2 -6x + 9 ___  HINT:START AT -1 AND INCREASE.
at x=-1
{{{y = 3(-1)^2 -6 *(-1) + 9}}}
{{{y = 3 + 6 + 9}}}
{{{y = 18}}}

at x=0
{{{y = 3*(0)^2 -6*(0) + 9}}}
{{{y = 9}}}

at x = 1
{{{y = 3(1)^2 -6 *(1) + 9}}}
{{{y = 3 - 6 + 9}}}
{{{y = 6}}}

at x =2
{{{y = 3(2)^2 -6 *(2) + 9}}}
{{{y = 3*4 - 12 + 9}}}
{{{y = 9}}}

So you can already see the minimum is somewhere between 0 and 2. As far as integers go, that is 1. In fact, the number IS 1.

Another way to check this is to plot it.
You can use a graphing calculator or something like geogebra. (geogebra is freee to download)
{{{graph(400,400, -10,10, -10,10, 3x^2-6x+9)}}}

Do the same process for the other problems


Grinding answers this way is never much fun. But is sometimes required. All it takes is a persistence. Happy grinding :)