Expert: Paul Klarreich - 11/23/2011

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
Questioner: kevin
Country: Beijing, China
Category: Calculus
Private: No
Subject: calculus
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)?
..........................................

This is an application of COMPLETING THE SQUARE:

f(x) = 2x^2 - 8x + 5

f(x) = 2(x^2 - 4x) + 5

f(x) = 2(x^2 - 4x     ) + 5

f(x) = 2(x^2 - 4x  + 4  - 4) + 5

f(x) = 2(x^2 - 4x  + 4) - 8 + 5

f(x) = 2(x^2 - 4x  + 4)  -  3

f(x) = 2(x - 2)^2  -  3

Take it from there.