Determine whether the given quadratic function has a minimum value or maximum value. Then find the
coordinates of the minimum or maximum point.
-$$f ( x ) = - x ^ { 2 } - 2 x - 8$$
A) maximum; $( - 1 , - 7 )$
B) minimum; $( - 1 , - 7 )$
C) minimum; $( - 7 , - 1 )$
D) maximum; $( - 7 , - 1 )$

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = -x^2 - 2x - 8$ has a leading coefficient that is negative ($-1$), indicating that the parabola opens downwards and thus has a maximum value. To find the coordinates of the maximum point, we use the vertex formula $x = -\frac{b}{2a}$, where $a = -1$ and $b = -2$. This gives $x = -\frac{-2}{2(-1)} = -1$. Substituting $x = -1$ into the function gives $f(-1) = -(-1)^2 - 2(-1) - 8 = -1 + 2 - 8 = -7$. Therefore, the maximum point is $(-1, -7)$.

Determine Whether the Given Quadratic Function Has a Minimum Value f(x)=−x2−2x−8f ( x ) = - x ^ { 2 } - 2 x - 8f(x)=−x2−2x−8

Determine Whether the Given Quadratic Function Has a Minimum Value $f ( x ) = - x ^ { 2 } - 2 x - 8$