Passage: Consider the curves y=x^2 and y=2|x| . Question: What is the number of points of intersection of the curves ?

Step-by-step solution

Equating the two given curves y = x^2 and y = 2|x| : x^2 = 2|x| Since x^2 = |x|^2 , the equation becomes: |x|^2 - 2|x| = 0 |x|(|x| - 2) = 0 This gives |x| = 0 or |x| = 2 . Solving for x , we get x = 0 , x = 2 , and x = -2 . The corresponding points of intersection are (0, 0) , (2, 4) , and (-2, 4) . The number of points of intersection is 3 . Answer: 3