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)