Determine whether the given quadratic function has a minimum value or maximum value. Then find the coordinates of
the minimum or maximum point.
-$f ( x ) = x ^ { 2 } - 2 x - 5$
A) maximum; $( 1 , - 6 )$
B) minimum; $( - 6,1 )$
C) minimum; $( 1 , - 6 )$
D) maximum; $( - 6,1 )$

Question

Quizplus · Accepted Answer

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where $a = 1$, $b = -2$, and $c = -5$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex (minimum point) can be found using the formula $(-b/2a, f(-b/2a))$. Substituting $a = 1$ and $b = -2$ gives the vertex as $(1, -6)$, confirming choice C.

Determine Whether the Given Quadratic Function Has a Minimum Value f(x)=x2−2x−5f ( x ) = x ^ { 2 } - 2 x - 5f(x)=x2−2x−5

Determine Whether the Given Quadratic Function Has a Minimum Value $f ( x ) = x ^ { 2 } - 2 x - 5$