Question

What is the quadratic formula for `f(b)=b^2 - 4b + 4 = 0`?

Answer 1

Rewriting `f(b)` as `f(x)` will permit you to use the standard formula with less confusion (since the standard quadratic formula uses `b` as one of its constants)

Explanation:

(since the given equation uses `b` as a variable, we will need to express the quadratic formula, which normally uses `b` as a constant, with some variant, `hatb`.

To help reduce confusion, I will rewrite the given `f(b)`as
`color(white)("XX")f(x)=x^2-4x+4=0`

For the general quadratic form:
`color(white)("XX")hatax^2+hatbx+hatc=0`
the solution given by the quadratic equation is
`color(white)("XX")x=(-hatb+-sqrt(hatb^2-4hatahatc))/(2hata)`

With `hata = 1`, `hatb=-4`, and `hatc=+4`
we get
`color(white)("XX")b=(x=)(4+-sqrt((-4)^2+4(1)(4)))/(2(1))`
as the quadratic formula