Originally Posted by

**mark** 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 $\displaystyle y = (2x + 3)(x - 1)^2$

the coefficient of $\displaystyle x^3$ is +2 so the shape of the graph is the same $\displaystyle y = x^3$ when x is numerically very large (this i understand). When $\displaystyle x = 0, y = (3)(-1)^2 = 3$ so the graph crosses the y- axis at 3 (this i understand also). When $\displaystyle y = 0, (2x + 3)(x - 1)^2 = 0$ so $\displaystyle x = \frac {3}{2} -$ and $\displaystyle x = 1$ (repeated root) so the graph crosses the x-axis at $\displaystyle x = \frac {3}{2} - $ and touches the x-axis at $\displaystyle x = 1$. When $\displaystyle x = 1, y = (1)(-2)^2 = 4 > 3$ 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