Question

How do you write the quadratic function `f(x) = x^2 -4x + 7` in vertex form?

Answer 1

`f(x) = (x-2)^2 +3`

Explanation:

If a standard quadratic has the form `y=ax^2+bx+c`, it can be rewritten into vertex form by completing the square. This means that we use `b/2a` to get an expression a(x+b/2a)^2 which equals `a(x^2+b/a*x+b^2/(4a^2))`. We then subtract `b^2/(4a^2)` and add`c` to finish the equation.
`f(x) = (x-2)^2 -4 +7`
`f(x) = (x-2)^2 +3`
This is vertex form, from which you can get that the vertex is at `(2,3)` - th epoint at which teh bracketed term is zero and therefore the expression is at its minimum value.