x Find the range of the quadratic function.
-$$f ( x ) = x ^ { 2 } - 2 x + 9$$
A) $[ 8 , \infty )$
B) $[ - 1 , \infty )$
C) $( - \infty , 8 ]$
D) $( - \infty , 6 ]$

Question

Quizplus · Accepted Answer

The vertex form of a quadratic function $f(x) = ax^2 + bx + c$ is $f(x) = a(x - h)^2 + k$, where $(h, k)$ is the vertex of the parabola. For $f(x) = x^2 - 2x + 9$, completing the square gives $f(x) = (x - 1)^2 + 8$. The vertex is $(1, 8)$, and since the coefficient of $x^2$ is positive, the parabola opens upwards. This means the minimum value of $f(x)$ is 8, at $x = 1$, and $f(x)$ increases without bound as $x$ moves away from 1. Therefore, the range of $f(x)$ is $[8, \infty)$.

X Find the Range of the Quadratic Function f(x)=x2−2x+9f ( x ) = x ^ { 2 } - 2 x + 9f(x)=x2−2x+9

X Find the Range of the Quadratic Function $f ( x ) = x ^ { 2 } - 2 x + 9$