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.

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).

Answer 1

Part A: f ( t ) = t² + 12 t - 19 =
= ( t² + 12 t + 36 ) - 36 - 18 = ( t + 6 )² - 54 ( the vertex form )
Part B : The vertex : ( - 6, - 54 ). This is the minimum, because the parabola is open up ( a > 0 ).
Part C : The axis of symmetry: t = - 6