Question 1091982
<br>I have not seen the idea of a point of symmetry being used with a polynomial function.  If you are talking about a point of symmetry in the usual sense, then the question you ask is easily answered.<br>
The given local minimum is 5 units to the right and 7 units below the point of symmetry; there must be a local maximum 5 units to the left and 7 units above the point of symmetry.  5 units left and 7 units up from (0,4) is at (-5,11)