Respuesta :

altavistard

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.

Only the third graph (option C) represents the graph of [tex]F(x) = \frac{1}{2} x^2[/tex]

The given function is:

[tex]F(x) = \frac{1}{2} x^2[/tex]

This graph is of the form [tex]y = ax^2[/tex] and it takes the shape of a parabola with center at (0, 0)

Only two of the graphs shown among the options have the center at the origin (0, 0), but only one is scaled by 0.5

Therefore, the graph of the function [tex]F(x) = \frac{1}{2} x^2[/tex] is plotted below

Learn more here: https://brainly.com/question/11279935

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