Question

The function f(t) = t2 4t − 14 represents a parabola.

Answer 1

Answer:

$f(t)=(t+2)^2 -18$  (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

$f(t)=(t+2)^2 -18$  (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

$f(t)=(t+2)^2 -18$

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