Find the range of the given function.
-$$f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }$$
A) $( - \infty , 0 ]$
B) $\left[ - \infty , - \frac { 53 } { 2 } \right]$
C) $\left[ \frac { 187 } { 2 } , \infty \right)$
D) $\left[ - \frac { 69 } { 2 } , \infty \right]$

Question

Quizplus · Accepted Answer

The function is a quadratic with a positive leading coefficient, so it opens upwards. The vertex form reveals the minimum value, which is $-\frac{69}{2}$, hence the range is $\left[ - \frac { 69 } { 2 } , \infty \right)$.

Find the Range of the Given Function f(x)=12x2−8x−52f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }f(x)=21​x2−8x−25​

Find the Range of the Given Function $f ( x ) = \frac { 1 } { 2 } x ^ { 2 } - 8 x - \frac { 5 } { 2 }$