The function f(t) = t2 4t − 14 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)

 (vertex form)

Vertex(-2,-18), minimum

axis of symmetry at x= -2

Step-by-step explanation:

f(t) = t^2+ 4t − 14

(a) Apply completing the square method

Take middle term +4, divide it by 2 and then square it

4/2= 2 , (2)^2 = 4

add and subtract 4

f(t) = (t^2+ 4t +4) -4− 14

 (vertex form)

(b)  Vertex form is y=a(x-h)^2 + k

vertex is (h,k)

when 'a' is positive then vertex is at minimum

when 'a' is negative then vertex is maximum

a=1, h=-2 and k= -18

vertex is (-2,-18)  , a= 1 that is positive

so it is a minimum

(c) Axis of symmetry at x=h

so axis of symmetry at x= -2

80π/3 or about 83.775

step-by-step explanation:

since a cone is 1/3 of a cylinder, we need to find the base's area. since area = πr^2, we get 16π. then, multiplying this by 5, we get 80π. dividing by 3, since the cone's volume is 1/3 of that of a cylinder's, we get 80π/3.

hope this !