What is the standard form of f(x)=(x-2)(x+3)+(x-1)^2 f(x)=(x−2)(x+3)+(x−1)2?

1 Answer
Konstantinos Michailidis
Feb 4, 2016

It is f(x)=2*(x-1/2)^2-9/2f(x)=2⋅(x−12)2−92

Explanation:

A quadratic function f(x) = a*x^2 + b*x + cf(x)=a⋅x2+b⋅x+c can be
expressed in the standard form
f(x) = a*(x − h)^2 + kf(x)=a⋅(x−h)2+k

Hence by expanding the given function we get

f(x)=2x^2-x-5=>f(x)=2(x^2-1/2x)-5=> f(x)=2*(x^2-2*1/4*x+(1/2)^2)-5=> f(x)=2*(x-1/2)^2-5+1/2=> f(x)=2*(x-1/2)^2-9/2

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