Question

determine whether the following statement is true or false. the graph of f(x) = (x + 5)^2 + 6 has its vertex at (5,6). choose the correct answer below. true false

Explanation:

Step1: Recall vertex form of parabola

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

Step2: Compare given function with vertex form

Given function is \( f(x) = (x + 5)^2 + 6 \). We can rewrite \( x + 5 \) as \( x - (-5) \). So comparing with \( f(x) = a(x - h)^2 + k \), we have \( h = -5 \) and \( k = 6 \). Thus, the vertex is \((-5, 6)\), not \((5, 6)\).

Answer:

False