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).