Question

consider the function f(x)=2x^2-8x+5.
a)express f(x) in the form of a(x-p)^2+q,where a,p,q are Z?
b)find the minimum value of f(x)?

Answer 1

2(x-2)^2 -3
min value is -3

Answer 2

sir i am dummy in calculus can you explain me detailed steps?

Answer 3

look for terms wid x
2x^2-8x
now we want smth of the form 2 (x-p)^2
hence take a two common
we get 2 (x^2-4x)

Answer 4

do u want me to explain the first part /second/both

Answer 5

both sir

Answer 6

ok then we got 2(x^2-4x)
x^2 -4x = (x-2)^2 -4 (By observation)
so put in the topmost equation and we get
2(x-2)^2 -8
now look at your question f(x)=2x^2-8x+5.
hence just add the +5 to what we just found out.
so what we are left with is 2(x-2)^2 -3

Answer 7

the second part is real simple and has no calcu lus involved
the square part is always positive or zero
hence
smth squared -3
will have min value when the squared part is zero givin f(x)=-3
which is its minimum

Answer 8

thank you very much for your reply

Answer 9

u r welcome