Find the domain and range of the function.
$y = ( x - 9 ) ^ { 2 } + 6$
A) $\text { Domain: } [ 9 , \infty ) \text {; Range: } [ - \infty , - 9 )$
B) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 6 , \infty )$
C) $\text { Domain: } ( - \infty , \infty ) \text {; Range: } [ 9 , \infty )$
D) $\text { Domain: } [ 6 , \infty ) \text {; Range: } [ - \infty , 6 )$

Question

Quizplus · Accepted Answer

The domain of a quadratic function is all real numbers $( - \infty , \infty )$, and since the vertex form is $y = a(x - h)^2 + k$ with $a > 0$, the range starts from the vertex's y-value ($k = 6$) and goes to infinity, hence $[6, \infty)$.

Find the Domain and Range of the Function y=(x−9)2+6y = ( x - 9 ) ^ { 2 } + 6y=(x−9)2+6

Find the Domain and Range of the Function $y = ( x - 9 ) ^ { 2 } + 6$