Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = 9 x ^ { 2 } + 36 x + 27$$
A) maximum at $( - 9 , - 2 )$
B) minimum at $( - 2,0 )$
C) maximum at $( - 9,0 )$
D) minimum at $( - 2 , - 9 )$

Question

Quizplus · Accepted Answer

The quadratic function is in the form $f(x) = ax^2 + bx + c$, where $a = 9$, $b = 36$, and $c = 27$. Since $a > 0$, the parabola opens upwards, indicating a minimum value. The vertex of the parabola, which gives the minimum value, can be found using the formula $(-b/2a, f(-b/2a))$. Substituting $a = 9$ and $b = 36$ into the formula gives the vertex as $(-2, -9)$, indicating a minimum at $(-2, -9)$.

Use the Quadratic Function to Determine If the Function Has f(x)=9x2+36x+27f ( x ) = 9 x ^ { 2 } + 36 x + 27f(x)=9x2+36x+27

Use the Quadratic Function to Determine If the Function Has $f ( x ) = 9 x ^ { 2 } + 36 x + 27$