Question

Which graph represents the function f(x) = (x – 5)2 + 3?

Answer 1

The graph is an upward-opening parabola with vertex at (5, 3) (shifted right 5 and up 3 from y = x^2). Key features to identify it:

- Vertex: (5, 3)
- Axis of symmetry: x = 5
- Opens upward with the same width as y = x^2 (leading coefficient 1)
- No real x-intercepts (minimum value y = 3)
- y-intercept: f(0) = 28

So choose the parabola whose lowest point is at (5,3), symmetric about x = 5, and has y ≥ 3.