Question

in the following exercise, find the coordinates of the vertex for the parabola defined by the given quadratic function.
$f(x) = -4(x + 9)^2 + 5$
the vertex is \\(\square\\). (type an ordered pair.)

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

Step2: Rewrite given function to match vertex form

Given \( f(x) = -4(x + 9)^2 + 5 \), we can rewrite \( (x + 9) \) as \( (x - (-9)) \). So comparing with \( f(x) = a(x - h)^2 + k \), we have \( h = -9 \) and \( k = 5 \).

Answer:

\((-9, 5)\)