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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.

User YoshiJaeger
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1 Answer

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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

User Blurfx
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