Question

question
determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
$f(x) = (x + 4)(x + 8)$

Explanation:

Step1: Expand the function

$f(x)=(x+4)(x+8)=x^2 + 12x + 32$

Step2: Identify a value

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

Step3: Find vertex x-coordinate

$x=-\frac{b}{2a}=-\frac{12}{2×1}=-6$

Step4: Calculate minimum value

$f(-6)=(-6)^2 + 12×(-6) + 32=36 - 72 + 32=-4$

Answer:

Minimum value is -4