hi, i've got another question on graphs, its part of a worked example, so it actually gives the answer but i don't understand:

sketch the graph of

the coefficient of

is +2 so the shape of the graph is the same

when x is numerically very large (this i understand). When

so the graph crosses the y- axis at 3 (this i understand also). When

so

and

(repeated root) so the graph crosses the x-axis at

and touches the x-axis at

. When

so the graph must turn in the second quadrant.

the last two points i don't understand, could someone tell me how you would tell if the graph crosses or only touches the x-axis and how you would tell by using x = -1 or x = + 1 or whatever that it turns in the second quadrant?

thanks for any help, mark

ps i tried putting the minus sign on the left for the fractions but it didn't work, i'm going to try to figure out how its done now