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. To find the minimum value, use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex. Substituting $b = 2$ and $a = 1$ gives $x = -\frac{2}{2(1)} = -1$. Then, substitute $x = -1$ into the original equation to find the y-coordinate (minimum value): $f(-1) = (-1)^2 + 2(-1) - 6 = 1 - 2 - 6 = -7$.

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