Final answer:
After substituting the point (-2, 4) into the given equations, it appears that none of the listed options a, b, c, or d match the given point. Therefore, the correct equation of the curve is not provided among the choices.
Step-by-step explanation:
To determine which equation corresponds to the curve that the point (-2, 4) lies on, we can substitute the x and y values into the given equation choices and see which one holds true. For each option, if substituting x = -2 and y = 4 results in a true statement, then that equation represents the curve.
- For option a, substituting gives 4 = (-2)² + 2, which simplifies to 4 = 4 + 2, which is false.
- Option b gives us 4 = 2(-2) - 8, simplifying to 4 = -4 - 8, which is also false.
- Substituting into option c yields 4 = 4(-2) + 2, which is 4 = -8 + 2, which is false as well.
- Finally, option d gives us 4 = -2(-2) + 4, which simplifies to 4 = 4 + 4, which is false.
None of the provided options lead to a true statement when substituted with the point (-2, 4). Thus, either there is an error in the question or the provided options, or the correct equation is not listed among the choices.