Thank you for the opportunity to help you with your question!

y=x^2-7x+6=(x-1)(x-6)

x1=1, x2=6

yes there is a minimum value for the given function because delta=b^2-4ac=49-24=25>0, the minimal value is when x=-b/2a=7/2, the minimal value is -6.25

Please let me know if you need any clarification. I'm always happy to answer your questions.