Question

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

Answer 1

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

Explanation:

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#