Final answer:
The point on the curve h(x) = x² - 4 that is closest to the point (-3, -4) is (-2, 0).
Step-by-step explanation:
The given curve is represented by the equation h(x) = x² - 4. To find the point on h(x) closest to the point (-3, -4), we need to find the point on the curve where the distance between the two points is minimized. This can be done by finding the x-coordinate of the point that minimizes the distance.
To find this, we can calculate the distance between the two points for each x-coordinate on the curve and find the minimum distance.
Substituting the values of x and y in the equation h(x) = x² - 4, we can calculate the distance for each x-coordinate and find the point that gives the minimum distance.
Calculating the distances for the given options, we find that the point (-2, 0) has the minimum distance to (-3, -4). Therefore, the answer is option a) (-2, 0).