Question

The function f(t)=t^2+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 its a maximum or minimum on the graph. How do you know? Part C: Determine the axis of Symmetry

Answer 1

The function in vertex form is $f(t) = (t+6)^{2} -54$ (refer to your other post I solved it there).
The general form of quadratic equations in vertex form is $f(x) = a(x-h)^{2} +k$, where (h, k) is the vertex of the parabola.
Here, a = 1, h = -6 and k = -54
Therefore, the vertex is (-6, -54) and it is a maximum because a = 1 is postive.