Question

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.

Answer 1

Considering the vertex of the parabola, the correct statement is given by:

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

What is the vertex of a quadratic equation?

A quadratic equation is modeled by:

$y = ax^2 + bx + c$

The vertex is given by:

$(x_v, y_v)$

In which:

• $x_v = -\frac{b}{2a}$

• $y_v = -\frac{b^2 - 4ac}{4a}$

Considering the coefficient a, we have that:

• If a < 0, the vertex is a maximum point, which means that the range is all real numbers less than or equal to $y_v$.

• If a > 0, the vertex is a minimum point, which means that the range is all real numbers greater than or equal to $y_v$.

In this problem, we have that:

• a = -1 < 0, hence the vertex is a maximum point.

• The vertex is (-2,9).

Hence the range is described by:

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

More can be learned about the vertex of a parabola at https://brainly.com/question/24737967

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