Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$
A) increasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
decreasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

B) increasing on $\left( - \infty , \frac { 1 } { 4 } \right)$
decreasing on $\left( \frac { 1 } { 4 } , \infty \right)$

C) decreasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
increasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

D) increasing on $\left( - \infty , - \frac { 43 } { 4 } \right)$
decreasing on $\left( - \frac { 43 } { 4 } , \infty \right)$

Question

Determine where the function is increasing and where it is decreasing.
-$$f ( x ) = - 4 x ^ { 2 } - 2 x - 11$$
A) increasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
decreasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

B) increasing on $\left( - \infty , \frac { 1 } { 4 } \right)$ 
decreasing on $\left( \frac { 1 } { 4 } , \infty \right)$

C) decreasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$
 increasing on $\left( - \frac { 1 } { 4 } , \infty \right)$

D) increasing on $\left( - \infty , - \frac { 43 } { 4 } \right)$
decreasing on $\left( - \frac { 43 } { 4 } , \infty \right)$

Quizplus · Accepted Answer

The function $f(x) = -4x^2 - 2x - 11$ is a downward-opening parabola because the coefficient of $x^2$ is negative. The vertex form of a parabola gives the maximum or minimum point, which is the turning point from increasing to decreasing or vice versa. The vertex $x$-coordinate can be found using $-\frac{b}{2a}$, where $a = -4$ and $b = -2$, giving $-\frac{-2}{2(-4)} = -\frac{1}{4}$. Since the parabola opens downward, it increases to the left of the vertex and decreases to the right, making the correct answer increasing on $\left( - \infty , - \frac { 1 } { 4 } \right)$ and decreasing on $\left( - \frac { 1 } { 4 } , \infty \right)$.

Determine Where the Function Is Increasing and Where It Is f(x)=−4x2−2x−11f ( x ) = - 4 x ^ { 2 } - 2 x - 11f(x)=−4x2−2x−11

Determine Where the Function Is Increasing and Where It Is $f ( x ) = - 4 x ^ { 2 } - 2 x - 11$