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)

For t²+6t-20=0 (to find the vertex, or rather the x intercepts), we can add 20 to both sides to get t²+6t=20. Since 6/2=3, we can square 3 to get 9. Adding 9 to both sides, we get t²+6t+9=20+9=29 = (t+3) ². Finding the square root of both sides, we get t+3=+-√ (29). Subtracting 3 from both sides, we get t=+-√ (29) - 3=either √ (29) - 3 or - √ (29) - 3. We have - √ (29) - 3 due to that t can either be negative or positive. Finding the average of the two numbers, we have

(√ (29) - 3) + (-√ (29) - 3./2=-6/2=-3, which is our t value of our vertex and since it's t² and based around t, that is our axis of symmetry. To find the y value of the vertex, we simply plug - 3 in for t to get 9 + (6*-3) - 20=9-18-20=-29, making our vertex (-3, - 29)