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

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Answer 1 · 2016-02-04T23:52:10

It is $f(x)=2*(x-1/2)^2-9/2$

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

Hence by expanding the given function we get

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

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