Find the range of the quadratic function.
-$$f ( x ) = ( x + 3 ) ^ { 2 } + 7$$
A) $[ 3 , \infty )$
B) $[ 7 , \infty )$
C) $[ - 3 , \infty )$
D) $[ - 7 , \infty )$

Question

Quizplus · Accepted Answer

The vertex form of the quadratic function is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. For the given function $f(x) = (x + 3)^2 + 7$, the vertex is $(-3, 7)$. Since the coefficient of the squared term is positive, the parabola opens upwards, making the minimum value of the function 7. Therefore, the range is $[7, \infty)$.

Find the Range of the Quadratic Function f(x)=(x+3)2+7f ( x ) = ( x + 3 ) ^ { 2 } + 7f(x)=(x+3)2+7

Find the Range of the Quadratic Function $f ( x ) = ( x + 3 ) ^ { 2 } + 7$