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

It is $f \left(x\right) = 2 \cdot {\left(x - \frac{1}{2}\right)}^{2} - \frac{9}{2}$

#### Explanation:

A quadratic function $f \left(x\right) = a \cdot {x}^{2} + b \cdot x + c$ 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