Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=x^{2}-10 x+33$
A) Maximum, 8
B) Maximum, 5
C) Minimum, 8
D) Minimum, 5

Question

Quizplus · Accepted Answer

Minimum, 8The quadratic function $f(x) = x^2 - 10x + 33$ is in the form $ax^2 + bx + c$, where $a = 1$, $b = -10$, and $c = 33$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. To find the minimum value, we use the vertex formula $x = -\frac{b}{2a}$ to find the x-coordinate of the vertex. Substituting $a = 1$ and $b = -10$, we get $x = -\frac{-10}{2(1)} = 5$. To find the minimum value (the y-coordinate of the vertex), we substitute $x = 5$ back into the original equation: $f(5) = (5)^2 - 10(5) + 33 = 25 - 50 + 33 = 8$.

Determine Whether the Given Quadratic Function Has a Maximum or Minimum