Question

The function f(t) = t2 + 12t − 18 represents a parabola.

Part A: Rewrite the function in vertex form by completing the square. Show your work. (6 points)

Part B: Determine the vertex and indicate whether it is a maximum or a minimum on the graph. How do you know? (2 points)

Part C: Determine the axis of symmetry for f(t). (2 points)

Answer 1

f(t) = t2 + 12t − 18 needs to be rewritten as f(t) = t^2 + 12t − 18, where the ^ represents exponentiation.

f(t) = t^2 + 12t − 18 represents a parabola. Complete the square to determine the vertex of this parabola.

Rewrite f(t) = t^2 + 12t − 18 as f(t) = t^2 + 12t − 18

Determine ONE HALF of the coefficient of t (which is 12).
Square your result. Add this to, and then subtract it from, t^2 + 12 t.

Show your work, please.