Question

What is the graph of the function? F(x) = 1/2x^2

Answer 1

F(x) = 1/2x^2 is a variation of the basic graph y = x^2 (the squaring function).

The graph of the squaring function has the shape of a parabola that opens up.  Its vertex is at (0,0).

The graph of F(x) = (1/2)x^2 has the same shape, but is compressed vertically by a factor of (1/2).   The vertex of F(x) = (1/2)x^2 is still (0,0).  That eliminates the first 2 possible answers.  Note that F(1) = (1/2)(1)^2 = 1/2.  The point (1, 1/2) is on the third graph, but not on the fourth.  Thus, the third graph is correct.