Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or
minimum value
-$$f ( x ) = 2 x ^ { 2 } - 4 x + 11$$
A) Maximum, 1
B) Minimum, 1
C) Maximum, 9
D) Minimum, 9

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = 2x^2 - 4x + 11$ is in the form $ax^2 + bx + c$, where $a = 2$, $b = -4$, and $c = 11$. 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 $a = 2$ and $b = -4$ gives $x = -\frac{-4}{2*2} = 1$. Then, substitute $x = 1$ into the original equation to find the minimum value: $f(1) = 2(1)^2 - 4(1) + 11 = 2 - 4 + 11 = 9$.

Determine Whether the Given Quadratic Function Has a Maximum or Minimum