What does g(x)=-3(x-1)^2+5 look like on a graph?

g(x)=-3(x-1)^2+5 is a modified version of y=x^2.  The graph of y=x^2 is that of a parabola that opens up.

h(x)= a(x-h)^2 + k is the most general form.  This has its vertex at (h,k).

Thus, g(x)=-3(x-1)^2+5 has its vertex at (1,5).

Draw y=x^2.  Then translate its vertex to (1,5).   Now, that "3" tells us to stretch the graph out vertically.  Lastlly, that "-" tells us to turn the previous graph upside down.

To graph this g(x)=-3(x-1)^2+5:
1) graph y=x^2
2) translate the vertex (0,0) of y = x^2 to (1,5).
3) invert the graph so that it opens down instead of up.
4) stretch the graph vertically by a factor of 3.
5)  if you wish, find the x-and y-intercepts and plot them.
6) draw the curve through these intercepts and (1,5).