Question

Use technology to construct an appropriate model of the data. (0,1), (1,-2), (2,-3), (3,-2), (4,1) f(x) = – x2 + 4 f(x) = x2 - 4 f(x) = - x2 + 4x - 1 f(x) = x2 - 4x + 1
a. f(x) = – (x+2)2 + 3B. f(x) = (x+2)2 + 3C. f(x) = – (x-2)2 - 3D. f(x) = (x-2)2 - 3

Answer 1

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