Question

Which points on the graph of y=4-x² are closest to the point (0, 2).

A) (1, 3)
B) (0, 4)
C) (-1, 3)
D) (2, 0)

Answer 1

To find the points on the graph of y = 4 - x² that are closest to the point (0, 2), use the distance formula to calculate the distances between the points. The closest points are (1, 3) and (0, 4).

Step-by-step explanation:

To find the points on the graph of y = 4 - x² that are closest to the point (0, 2), we need to calculate the distance between these points. The distance formula is √((x2-x1)² + (y2-y1)²). Substituting the values, the distances for each answer choice are: A) √((1-0)² + (3-2)²) = 2; B) √((0-0)² + (4-2)²) = 2; C) √((-1-0)² + (3-2)²) = √(1 + 1) = √2; D) √((2-0)² + (0-2)²) = √(4 + 4) = √8.

The closest points to (0, 2) are therefore A) (1, 3) and B) (0, 4) since they have the smallest distance of 2.