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