Question 905138
{{{g}}} is just the name of the function of {{{x}}. 
When you graph the function you usually use {{{y}}} as the variable.
{{{y=5(x-3)^2+10}}}
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{{{graph(300,300,-7,7,-2,12,5(x-3)^2+10)}}}
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OK, so what does vertex form tell you. 
The vertex is at (3,10).
Since {{{5>0}}}, the parabola opens upwards at the value at the vertex is the minimum value of the function. 
So {{{g(x)>=10}}} for all {{{x}}}.
Since {{{10>0}}} then {{{g(x)>0}}} for all {{{x}}}.
Yes, min value is {{{g(3)=10}}} and there is no max value.