let $f(x)=x^{2}-8x + 19$. what is the minimum value of the function? enter your answer in the box.

let $f(x)=x^{2}-8x + 19$. what is the minimum value of the function? enter your answer in the box.

let $f(x)=x^{2}-8x + 19$. what is the minimum value of the function? enter your answer in the box.

Answer

Answer:

3

Explanation:

Step1: Rewrite in vertex - form

$f(x)=x^{2}-8x + 19=(x - 4)^{2}-16 + 19=(x - 4)^{2}+3$

Step2: Identify the minimum value

For a quadratic function $y=a(x - h)^{2}+k$ with $a = 1>0$, the vertex is $(h,k)$. The minimum value occurs at the vertex. Here, $k = 3$. So the minimum value of $f(x)$ is 3.