Question

How would I write the function f(x)=(x-2)^2-3 in standard form? like, I don't really understand what I'm doing here.

Answer 1

By definition, a Quadratic function written in Standard form, is:

$y=ax^2+bx+c$

Where "a", "b" and "c" are Real numbers (the lead coefficient "a" cannot be zero).

For this case, you have the following Quadratic function written in Vertex form:

$f(x)=(x-2)^2-3$

By definition, you have that:

$(a-b)^2=a^2-2ab+b^2$

Then, applying that formula, you can simplifiy the function and write it in Standard form:

$\begin{gathered} f(x)=(x^2-2(x)(2)+2^2)-3 \\ f(x)=x^2-4x+4-3 \\ f(x)=x^2-4x+1 \end{gathered}$

Therefore, the answer is:

$f(x)=x^2-4x+1$