Question

the axis of symmetry for the function \\(f(x) = -x^2 - 10x + 16\\) is \\(x = -5\\). what are the coordinates of the vertex of the graph?

\\((-5, 41)\\)
\\((-5, 56)\\)
\\((-5, 76)\\)
\\((-5, 91)\\)

Explanation:

Identify the given information

Using the Axis of Symmetry knowledge point
The axis of symmetry is given as \(x = -5\).
The quadratic function is:

$$f(x) = -x^2 - 10x + 16$$

Determine the vertex coordinates

Using the Quadratic Vertex knowledge point
The \(x\)-coordinate of the vertex lies on the axis of symmetry, so \(h = -5\).
To find the \(y\)-coordinate \(k\), evaluate \(f(-5)\):

$$
LATEXBLOCK0
$$

Thus, the vertex is \((-5, 41)\).

Answer:

• (A) \((-5, 41)\) (Correct answer)
• (B) \((-5, 56)\)
• (C) \((-5, 76)\)
• (D) \((-5, 91)\)