Question 1058130
#2,
(3,7) is not any x-intercept.
Vertex is the minimum value and you have no information given to find x-value for the minimum.  Minimum,  (?, -8).  Not a definite point.


#3,
Not enough information to determine the function.  The leading coefficient stays unknown and not determinable.


#1
This can be solved.
{{{y=a(x-4)^2-2}}}
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{{{a(x-4)^2=y+2}}}
{{{a=(y+2)/(x-4)^2}}}
Substitute the y-intercept:
{{{a=(2+2)/(0-4)^2}}}
{{{a=4/16=1/4}}}
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{{{highlight(y=(1/4)(x-4)^2-2)}}}