Question

The image shows a geometric representation of the function f(x) = x2 – 2x – 6 written in standard form.

Answer 1

The given polynomial is f(x) = x² - 2x - 6

Rewrite the function by completing the square.
f(x) = [x² - 2x] - 6
      = [(x-1)² - 1] - 6
      = (x-1)² - 7

In vertex form,
f(x) = (x-1)² - 7

The vertex is located at (1, -7).
Because the leading coefficient is +1, the curve opens upward.

Answer: f(x) = (x - 1)² - 7