Use the quadratic function to determine if the function has a maximum or minimum value and then find this maximum or minimum value.
-$$f ( x ) = 3 x ^ { 2 } + 3 x - 9$$
A) minimum at $\left( - \frac { 1 } { 2 } , - \frac { 39 } { 4 } \right)$
B) minimum at $\left( - \frac { 39 } { 4 } , - \frac { 1 } { 2 } \right)$
C) maximum at $\left( - \frac { 1 } { 2 } , - \frac { 39 } { 4 } \right)$
D) maximum at $\left( - \frac { 39 } { 4 } , - \frac { 1 } { 2 } \right)$

Question

Quizplus · Accepted Answer

Since the coefficient of $x^2$ is positive (3), the parabola opens upwards, indicating a minimum value. The vertex of the parabola, given by $(- \frac{b}{2a}, f(- \frac{b}{2a}))$, where $a = 3$, $b = 3$, and $c = -9$, is $(- \frac{1}{2}, - \frac{39}{4})$.

Use the Quadratic Function to Determine If the Function Has f(x)=3x2+3x−9f ( x ) = 3 x ^ { 2 } + 3 x - 9f(x)=3x2+3x−9

Use the Quadratic Function to Determine If the Function Has $f ( x ) = 3 x ^ { 2 } + 3 x - 9$