Question

determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
$f(x) = (x - 8)^2 - 3$

Explanation:

Step1: Identify vertex form

Quadratic function is \(f(x)=(x-8)^2 - 3\), vertex form \(a(x-h)^2 + k\)

Step2: Check coefficient a

\(a=1>0\), so parabola opens up (has minimum)

Step3: Find minimum value

Minimum at vertex \((h,k)=(8,-3)\), value is \(k=-3\)

Answer:

Minimum value, -3