The function f(t) = t2 + 6t − 20 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).

Step-by-step explanation:

Note that the equation should be

f(t) = t^2 + 6t - 20

A. Completing the square

coefficient of the t term: 6

divide it in half: 3

square it: 3²

add 3² to complete the square and subtract 3² to keep the equation balanced:

f(t) = (t² + 6t + 3²) - 3² - 20

f(t) = (t+3)² - 29. This is the equation in vertex form.

B. Vertex (-3, -29)

The leading coefficient of the equation is +1. Since the leading coefficient is positive, the parabola opens upwards. Therefore, the vertex is a minimum.

The axis of symmetry is the vertical line passing through the vertex: x = -3

-2x + 7 = 7

subtract 7 from both sides.

-2x = 0

divide both sides by -2.

x = 0