Determine whether the given quadratic function has a maximum or minimum value. Then find that maximum or minimum value.
-$f(x)=5(x-6)^{2}-7$
A) Minimum, -7
B) Minimum, 7
C) Minimum, 6
D) Maximum, - 7

Question

Quizplus · Accepted Answer

The given quadratic function is in vertex form, $f(x) = a(x-h)^2 + k$, where $a = 5$, $h = 6$, and $k = -7$. Since $a > 0$, the parabola opens upwards, indicating a minimum value at the vertex. The vertex of the parabola, given by the point $(h, k)$, is $(6, -7)$. Therefore, the minimum value of the function is $-7$.

Determine Whether the Given Quadratic Function Has a Maximum or Minimum