Let fxx212x44 Find the vertex State the range of the functio

Let f(x)=x^2+12x+44. Find the vertex. State the range of the function. On what interval is the function increasing?

Solution

f(x)=x^2 +12x+44

let f(x)=y

y= x^2+12x+44

y=x^2+2(6x) +36 + 8

y-8 = (x+6)^2

so vertex is (-6,8)

b).Range of function is R

range = (-infinite, infinite)

c)

finding f\'(x) =2x+12

x =-6

finding f\'\'(x) = 2

the interval it is increasing is (-6, infinite)