Explanation
To find the number of points of intersection, we set the equations equal to each other:
x2=2∣x∣
Since x2=∣x∣2, we can rewrite the equation as:
∣x∣2−2∣x∣=0
Factoring out ∣x∣:
∣x∣(∣x∣−2)=0
This gives us two possible cases for ∣x∣:
∣x∣=0⟹x=0
∣x∣=2⟹x=2 or x=−2
Now, we find the corresponding y-coordinates for these x-values using y=x2:
If x=0, y=02=0. The point is (0,0).
If x=2, y=22=4. The point is (2,4).
If x=−2, y=(−2)2=4. The point is (−2,4).
The points of intersection are (0,0), (2,4), and (−2,4). Counting these, we find there are exactly 3 points of intersection.
Therefore, the correct option is (b).
