In order to graph the parabola, first let's identify the x-coordinate of the vertex.
To do so, we can use the formula below, after identifying the parameters a, b and c from the standard form of the equation:
[tex]\begin{gathered} x_v=\frac{-b}{2a} \\ \\ y=ax^2+bx+c \\ a=-3,b=0,c=3 \\ \\ x_v=\frac{-0}{2\cdot(-3)}=0 \end{gathered}[/tex]
Now, let's calculate the points using x = -2, x = -1, x = 0, x = 1 and x = 2:
[tex]\begin{gathered} x=-2\colon \\ y=-3(-2)^2+3=-3\cdot4+3=-12+3=-9 \\ x=-1\colon \\ y=-3(-1)^2+3=-3\cdot1+3=0 \\ x=0\colon \\ y=-3\cdot0^2+3=0+3=3 \\ x=1\colon \\ y=-3\cdot1^2+3=0 \\ x=2\colon \\ y=-3\cdot2^2+3=-12+3=-9 \end{gathered}[/tex]
Graphing these points and the corresponding parabola, we have:
