If the point (7, 6) lies on the graph of y = (x − 5)^2 + k, where k is some constant, which other point must also lie on the same graph?

Question

The choices you can choose from are

a. (−5, 6)

b. (3, 6)

c. (5, 6)

d. (9, 6)

Answer 1

The graph of y = (x-5)² + k is a parabola opening upward with axis of symmetry x = 5.

Since (7,6) is 2 units to the right of the line x = 5 and is 6 units above the x-axis, then by symmetry,

the point (3, 6) [two units to the left of the axis of symmetry and 6 units above the x-axis] must also be on the graph.