# Question #92542

##### 1 Answer

May 14, 2016

See explanation...

#### Explanation:

Note that vertex form of a vertical parabola can be written:

#y = a(x-h)^2+k#

where

We are given:

#f(x) = 1-x#

#g(x) = 2x^2-9#

#h(x) = (g @ f)(x)#

#= g(f(x))#

#= g(1-x)#

#= 2(1-x)^2-9#

#= 2(1-2x+x^2)-9#

#= 2-4x+2x^2-9#

#= color(blue)(2x^2-4x-7)#

#= 2(x^2-4x+4)-15#

#= 2(x-2)^2-15#

#= color(blue)(2(x+(-2))^2+(-15))#

The minimum value of

If

#color(blue)(k(x) = 2(x+1)^2-5)#