Question

Please help me with this problem:Let f(x)=x^2−6x+13 .What is the vertex form of f(x)?What is the minimum value of f(x)?Enter your answers in the boxes.Vertex form: f(x)= ___Minimum value of f(x): __

Answer 1

Given the quadratic function f(x) = x²-6x+13, notice that we can write it like this:

$\begin{gathered} f(x)=x²-6x+13=x²-6x+9+4=(x-3)²+4 \\ \Rightarrow f(x)=(x-3)²+4 \end{gathered}$

thus, the vertex form of f(x) is (x-3)²+4.

The minimum value of f will be on the vertex of the function. Therefore, the minimum value of f(x) is 4