quadratic equations

i) f(x)
= -(x+3)^2 +4

because -(x+3)^2 smaller than or equal to 0
therefore f(x)=-(x+3)^2 +4 is smaller than or equal to 4


ii) g(x)
= (2x-3)^2 +3-x
= 4x^2 -13x+12
= 4(x-13/8)^2+23/16
because 4(x-13/8)^2 is larger than or equal to 0
therefore g(x) = (2x-3)^2 +3-x is larger than or equal to 23/16



sorry, as i don't know how to enter those symbols, i have to type them by words. sorry...

My maths aren't very good... so i don't know will this help
I am having my exams about this topic
I am not sure which range you are asking for...
i) f(x) = -(x+3)^2 +4
if it is asking for f(x)
..we can say since the vertex is (-3,4)....and it opens downward...
therefore the range of f(x) is x<-3
for all values of x

ii) g(x) = (2x-3)^2 +3-x
g(x) = 4x^2 - 13x + 12
complete square.....then find the vertex