Think about how you might sketch a parabola.
Do the sides of a parabola ever curve in as in the figure at the right? Explain your reasoning.
No, because there is only one
-value for every -value in a parabola.
Do the sides of the parabola approach straight vertical lines as shown in the figure at right? (In other words, do parabolas have vertical asymptotes?) Give a reason for your answer.
The domain of a parabola is all real numbers, so the graph must extend all the way left and right. Hence it never goes straight up.