The answer choices tell you this is a parabola.
The given points tell you it opens upward and the vertex is (2, -3).
Your knowledge of the vertex form of the equation is the only "technology" that you need. The vertex form is
y = a(x - h)² + k . . . . . for vertex (h, k)
The fact that the y-value is 1 more than its vertex value when |x-2| = 1 tells you the scale factor "a" is 1.
You can write the model as
D. f(x) = (x -2)² - 3
The given points tell you it opens upward and the vertex is (2, -3).
Your knowledge of the vertex form of the equation is the only "technology" that you need. The vertex form is
y = a(x - h)² + k . . . . . for vertex (h, k)
The fact that the y-value is 1 more than its vertex value when |x-2| = 1 tells you the scale factor "a" is 1.
You can write the model as
D. f(x) = (x -2)² - 3