Find the range of the quadratic function in interval notation.
-$$f ( x ) = 4 x ^ { 2 } - 2 x - 9$$
A) $\left[ \frac { 1 } { 4 } , \infty \right)$
B) $\left( - \infty , - \frac { 37 } { 4 } \right]$
C) $\left[ - \frac { 37 } { 4 } , \infty \right)$
D) $\left( - \infty , \frac { 1 } { 4 } \right]$

Question

Quizplus · Accepted Answer

The quadratic function $f(x) = 4x^2 - 2x - 9$ opens upwards (since the coefficient of $x^2$ is positive), and its vertex gives the minimum point of the function. To find the vertex, use the formula $x = -\frac{b}{2a}$, where $a = 4$ and $b = -2$. This gives $x = \frac{1}{4}$. Substituting $x = \frac{1}{4}$ into the function gives the minimum value $f\left(\frac{1}{4}\right) = 4\left(\frac{1}{4}\right)^2 - 2\left(\frac{1}{4}\right) - 9 = -\frac{37}{4}$. Therefore, the range is $\left[ -\frac{37}{4}, \infty \right)$.

Find the Range of the Quadratic Function in Interval Notation f(x)=4x2−2x−9f ( x ) = 4 x ^ { 2 } - 2 x - 9f(x)=4x2−2x−9

Find the Range of the Quadratic Function in Interval Notation $f ( x ) = 4 x ^ { 2 } - 2 x - 9$