Question

Which graph represents f(x)=1/2x^2 ?

Answer 1

`f(x)=(1)/(2)x^2\\\\for\ x=0\to f(0)=(1)/(2)(0)=0\to(0,\ 0)\\\\for\ x=\pm1\to f(\pm1)=(1)/(2)(\pm1)^2=(1)/(2)(1)=(1)/(2)\to\left(-1,\ (1)/(2)\right);\ \left(1;\ (1)/(2)\right)\\\\for\ x=\pm2\to f(\pm2)=(1)/(2)(\pm2)^2=(1)/(2)(4)=2\to(-2,\ 2);\ (2,\ 2)\\\\for\ x=\pm4\to f(\pm4)=(1)/(2)(\pm4)=\dfraC{1}{2}(16)=8\to(-4,\ 8);\ (4,\ 8)`

Answer 2

See below.

Explanation:

The one that looks like the attachment.

It is vertically shortened from f(x) = x^2, so appears wider than f(x) = x^2 does. The vertex is still at (0, 0), it still opens upward, and it remains symmetrical about the y-axis.