Question

The function g(n) = n2 - 6n + 16 represents a parabola.
Part A: Rewrite the function in vertex form by completing the square. Show your work
Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know?
Part C: Determine the axis of symmetry for g(n).

Answer 1

Hi,

Part A:

$g(n) = n^2 - 6n + 16 \\=(n^2-2*3*n+3^2+7)\\=(n-3)^2+7$

Part B;

Vertex is (3,7)

As the coefficient of n² is positive , the vertex is a minimum.

Part C:

Axis of symmetry is n=3