Find the domain and range of the quadratic function whose graph is described.
-The maximum is $- 3$ at $x = - 1$
A) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 3 ]$
B) Domain: $( - \infty , - 1 ]$
Range: $( - \infty , - 3 ]$
C) Domain: $( - \infty , \infty )$
Range: $[ - 3 , \infty )$
D) Domain: $( - \infty , \infty )$
Range: $( - \infty , - 1 ]$

Question

Quizplus · Accepted Answer

The domain of any quadratic function is all real numbers, $( - \infty , \infty )$, because you can input any real number for $x$. The range is determined by the maximum or minimum value the function can take. Since the maximum value is $-3$ and it opens downwards (implied by the presence of a maximum), the function's values can be anything less than or equal to $-3$, hence $( - \infty , - 3 ]$.

Find the Domain and Range of the Quadratic Function Whose −3- 3−3

Find the Domain and Range of the Quadratic Function Whose $- 3$