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.

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 f (t).

For

f (x) = a (x-h) ²+k

vetex is (h, k)

axis of symmetry is x=h

when a is positive, the graph opens up and the vertex is a minimum

when a is negative, the graph opens down and the vertex is a maximum

f (t) = (t²+12t) - 18

take 1/2 of 12 and square it and add negative and positive of it inside (36)

f (t) = (t²+12t+36-36) - 18

factoer perfect square

f (t) = ((t+6) ²-36) - 18

expand

f (t) = (t+6) ²-36-18

f (t) = (t+6) ²-54

vertex form

f (t) = 1 (t - (-6)) ² + (-54)

vertex is (-6,-54)

1 is positive, it is a minimum

axis of symmetry is x=-6

A. f (t) = (t+6) ²-54

B. (-6,-54), minimum

C. x=-6