Question #92542
1 Answer
See explanation...
Explanation:
Note that vertex form of a vertical parabola can be written:
y = a(x-h)^2+ky=a(x−h)2+k
where
We are given:
f(x) = 1-xf(x)=1−x
g(x) = 2x^2-9g(x)=2x2−9
h(x) = (g @ f)(x)h(x)=(g∘f)(x)
= g(f(x))=g(f(x))
= g(1-x)=g(1−x)
= 2(1-x)^2-9=2(1−x)2−9
= 2(1-2x+x^2)-9=2(1−2x+x2)−9
= 2-4x+2x^2-9=2−4x+2x2−9
= color(blue)(2x^2-4x-7)=2x2−4x−7
= 2(x^2-4x+4)-15=2(x2−4x+4)−15
= 2(x-2)^2-15=2(x−2)2−15
= color(blue)(2(x+(-2))^2+(-15))=2(x+(−2))2+(−15)
The minimum value of
If
color(blue)(k(x) = 2(x+1)^2-5)k(x)=2(x+1)2−5