Determine, without graphing, whether the given quadratic function has a maximum value or a minimum value and then
find that value.
-$$f ( x ) = x ^ { 2 } + 2 x - 6$$
A) minimum; - 7
B) maximum; - 1
C) maximum; - 7
D) minimum; - 1

Question

Quizplus · Accepted Answer

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where $a = 1$, $b = 2$, and $c = -6$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex formula gives the minimum value: $$f(x) = -\frac{b^2}{4a} + c = -\frac{(2)^2}{4(1)} - 6 = -1 - 6 = -7.$$

Determine, Without Graphing, Whether the Given Quadratic Function Has a Maximum