Question

question
determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
$f(x) = -2x^2 - 12x - 19$

Explanation:

Step1: Identify coefficient a

For \(f(x) = ax^2 + bx + c\), \(a = -2\) (negative, so maximum)

Step2: Calculate x-coordinate of vertex

\(x = -\frac{b}{2a} = -\frac{-12}{2(-2)} = -3\)

Step3: Find maximum value

Substitute \(x=-3\) into \(f(x)\):
\(f(-3) = -2(-3)^2 -12(-3) -19 = -18 +36 -19 = -1\)

Answer:

Maximum value is -1