Question 1050231
The description is inconsistent and therefore makes no sense.  Look at your graph carefully again and adjust your description.  Is the vertex a minimum or a maximum?  What quadrant is it in, or if not, on which part of which axis is it?  In which quadrants are/is the left branch of the parabola?  In which quadrant is/are the right branch of the parabola?



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Your adjusted description:
The graph pictured is a parabola, pointing upward with its minimum/vertex in quadrant 4, left side mostly in quadrant 2, right side mostly in quadrant 1, and the minimum in quadrant 4 is slightly to the right of the y axis. 


The graph will cross the x-axis in two places.  One at a negative x value and the other at a positive x value.  The minimum being in quadrant 4 means that the k value is negative.  The parabola having a MINIMUM for its vertex means that {{{a>0}}}.




Let me use roots r and s for the roots or x-axis intercepts, and using your factored form, {{{f(x)=a(x-r)(x-s)}}} ----------- this is one of the typical formats for a quadratic function.



Using that form and your parabola as described,
{{{system(a>0,r>0,s<0)}}}
and you can take the r and s variables to help in their meaning as r for RIGHTMOST, and s for SINISTER (meaning to the left or leftmost).



Also according to how you described, <i>the minimum in quadrant 4 is slightly to the right of the y axis</i>, indicates that {{{abs(r)>abs(s)}}}.  That along with {{{s<r}}}  (but do not becomes confused about order and size).



You can understand this parabola and the values according to the standard form  {{{f(x)=a(x-h)+k}}}.
The vertex would be (h,k), and here, {{{k<0}}} and {{{h>0}}}.
You already know that {{{a>0}}}.