Determine whether there is a maximum or minimum value for the given function, and find that value.
-$$f ( x ) = x ^ { 2 } + 6 x - 1$$
A) Maximum: $- 10$
B) Maximum: 0
C) Minimum: $- 3$
D) Minimum: $- 10$

Question

Quizplus · Accepted Answer

The given function is a quadratic function of the form $f(x) = ax^2 + bx + c$, where $a = 1$, $b = 6$, and $c = -1$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex of the parabola, given by $(-b/2a, f(-b/2a))$, is the point where this minimum occurs. Calculating the x-coordinate of the vertex gives $-b/2a = -6/(2*1) = -3$. Substituting $x = -3$ into the original function to find the minimum value: $f(-3) = (-3)^2 + 6(-3) - 1 = 9 - 18 - 1 = -10$.

Determine Whether There Is a Maximum or Minimum Value for the Given