Question

algebra concepts and connections - plc modeling and analyzing quadratic functions: quadratic functions the function ( f(x) = -x^2 - 4x + 5 ) is shown on the graph. which statement about the function is true? the domain of the function is all real numbers less than or equal to 9. the domain of the function is all real numbers less than or equal to -2. the range of the function is all real numbers less than or equal to 9.

Explanation:

Step1: Analyze domain of quadratic function

For the function $f(x) = -x^2 -4x +5$, quadratic functions have no restrictions on input $x$, so the domain is all real numbers.

Step2: Analyze range of quadratic function

The parabola opens downward (coefficient of $x^2$ is $-1<0$), with vertex at $(-2,9)$. The maximum $y$-value is 9, so $y \leq 9$.

Step3: Match with given statements

Compare the domain/range findings to the options: the range statement matches.

Answer:

The range of the function is all real numbers less than or equal to 9.