-first consider what is means to touch the x-axis: being not the x-axis means that y is equal to zero.

-so you set up an equation were 0=-2x^2+x-3

-and the right side is factorable (-2x+3)(x+1) they are two distinct factors thus two answers when y=0 thus two point in common with the x-axis

-Notice that the number in front of the x^2. It is a negative number so it means that it is making an "n" shape and not an "u" shape.

-if it is an n shaped and the it crosses the x-axis twice, the vertex has to be above the axis. Because if it was below it will never cross the x-axis.