Find the range of the given function.
-$$f ( x ) = x ^ { 2 } - 14 x + 58$$
A) $[ 7 , \infty )$
B) $( - \infty , 0 ]$
C) $[ - 7 , \infty )$
D) $[ 9 , \infty )$

Question

Quizplus · Accepted Answer

The function is a quadratic in the form $f(x) = ax^2 + bx + c$ with $a = 1$, $b = -14$, and $c = 58$. The vertex form reveals the minimum point, which is at $x = -\frac{b}{2a} = 7$. Substituting $x = 7$ into the function gives $f(7) = 9$. Since the parabola opens upwards, the range is $[9, \infty)$.

Find the Range of the Given Function f(x)=x2−14x+58f ( x ) = x ^ { 2 } - 14 x + 58f(x)=x2−14x+58

Find the Range of the Given Function $f ( x ) = x ^ { 2 } - 14 x + 58$