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)
Part A: f ( t ) = t² + 12 t - 19 ( t² + 12 t + 36 ) - 36 - 18 ( t + 6)² - 54 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.