The function f(x) = –x2 – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down. It goes through (negative 5, 0), has a vertex at (negative 2, 9), and goes through (1, 0). Which statement about the function is true?
The domain of the function is all real numbers less than or equal to −2.
The domain of the function is all real numbers less than or equal to 9.
The range 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.

The vertex of the parabola is at (–2, 9). Then the range of the function is all real numbers less than or equal to 9. Then option D is correct.

What is the parabola?

It is the locus of a point that moves so that it is always the same distance from a non-movable point and a given line. The non-movable point is called focus and the non-movable line is called the directrix.

The function f(x) = –x² – 4x + 5 is shown on the graph. On a coordinate plane, a parabola opens down.

f(x) = –x² – 4x + 5

Add and subtract 4, then we have

f(x) = –x² – 4x – 4 + 4 + 5

f(x) = –(x² + 4x + 4) + 4 + 5

f(x) = –(x + 2)² + 9

Then the vertex of the parabola is at (–2, 9). Then the range of the function is all real numbers less than or equal to 9.

More about the parabola link is given below.

https://brainly.com/question/8495504