Question

question
determine whether the quadratic function shown below has a minimum or maximum, then determine the minimum or maximum value of the function.
$f(x) = -2x^2 - 12x - 17$
answer attempt 1 out of 2
the value is
minimum
maximum

Explanation:

Step1: Identify vertex direction

For $f(x)=ax^2+bx+c$, $a=-2<0$, so parabola opens downward, has a maximum.

Step2: Find x-coordinate of vertex

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

Step3: Compute maximum value

Substitute $x=-3$ into $f(x)$:

$$\begin{align*} f(-3)&=-2(-3)^2 -12(-3) -17\\ &=-2(9)+36-17\\ &=-18+36-17 \end{align*}$$

Answer:

The function has a maximum value, and the maximum value is 1.