Problem: The graphs of y=x−2x2−4​ and y=2x intersect in.
Answer Choices:
A. 1 point whose abscissa is 2
B. 1 point whose absci$sa is 0
C. no points
D. two distinct points
E. two identical points
Solution:
Since y=(x2−4)/(x−2)=(x−2)(x+2)/(x−2)=x+2 (for xî€ =2, i.e. yî€ =4), then y=(x2−4)/(x−2) is a straight line with the point (2,4) deleted. The straight line y=2x crosses the first line in the deleted point. ∴(C) is the correct choice.