The vertex occurs a the point (4,-9) The easiest way to do this is to draw the graph, or create a table of test values. When you do this, you will see as you increase the value of X, the value of Y continue to shrink until u hit X=4. The graph starts to increase in. So you know that is the vertex. In general, all functions of the form ax^2 +bx + c will have only one vertex. So you can apply this method.
you need to know the mass of the jewelry box before you can know the volume but i can help you multiply th 15 and the 10 to get the mass most likely then divided what you have from 15 x 10 by the depth and you have your answer just be sure to round it off!