Answer
See the picture below.
Work Step by Step
By calculating the values of $f(x)=x^2+3$ (with blue) and $g(x)=x^2$ (with red) we can see that for every corresponding x-value, each $f(x)$ value is 3 greater than the $g(x)$ value.
For drawing the exact parent graph, here is the table of values:
$g(-2)= -2^2=4$
$g(-1)= -1^2=1$
$g(0)= 0^2=0$
$g(1)= 1^2=1$
$g(2)=2^2=4$
Therefore the graph of $f(x)$ is exactly the same as the graph of $g(x)=x^2$ but translated 3 units up.
For drawing the exact graph of $f(x)$ here is the table of values of the given function:
$f(-2)=(-2)^2+3=7$
$f(-1)=(-1)^2+3=4$
$f(0)=(0)^2+3=3$
$f(1)=(1)^2+3=4$
$f(2)=(2)^2+3=7$