1. (10 points) From the parabolas listed below, select those for which points $A(-1,-1)$ and $B(0,2)$ lie on the same side.
a) $y=2 x^{2}+4 x$

б) $y=x^{2} / 2-x-3 / 2$;

в) $y=-x^{2}+2 x-1$;
2) $y=-x^{2}-4 x-3$;

д) $y=-x^{2}+3$

е) none of the listed answers are correct.

Mark the correct answer, no need to provide the solution.
Answer: a), c) and d).

Solution. Transform the equations of the parabolas by completing the square:

1) $2 x^{2}+4 x=2(x+1)^{2}-2-$ the vertex of the parabola is the point with coordinates $(-1,-2)$, the branches of this parabola are directed upwards; it is easy to see that both given points lie inside the parabola;
2) $x^{2} / 2-x-3 / 2=(x-1)^{2} / 2-2-$ in this case, the vertex is the point $(1,-2)$, the branches are also directed upwards, but the left branch intersects the x-axis at the point -1, thus, the given points lie on opposite sides of the parabola;
3) $-x^{2}+2 x-1=-(x-1)^{2}-$ the vertex is at the point $(1,0)$, the branches are directed downwards, the left branch intersects the y-axis at the point -1, therefore, both given points lie outside the parabola;
4) $-x^{2}-4 x-3=-(x+2)^{2}+1-$ the vertex is at the point $(-2,1)$, the branches are directed downwards, the right branch intersects the x-axis at the point -1, so the given points lie on opposite sides of the parabola;
5) for the parabola $-x^{2}+3$ the vertex is at the point $(0,3)$, the branches are directed downwards, so in this case, both given points lie inside the parabola.