Question

1. what is the vertex of the graph of the function $f(x) = x^2 + 6x + 9$?

a $(-3, 0)$ b $(0, -3)$
c $(0, 3)$ d $(3, 0)$
envision® integrated mathematics ii

Explanation:

Step1: Rewrite the function in vertex form

The function is \( f(x) = x^2 + 6x + 9 \). Notice that this is a perfect square trinomial, so we can factor it as \( f(x)=(x + 3)^2 \). The vertex form of a quadratic function is \( f(x)=a(x - h)^2 + k \), where \((h,k)\) is the vertex. In our case, \( a = 1 \), \( h=-3 \) (because it's \( x - (-3)=x + 3 \)), and \( k = 0 \).

Step2: Identify the vertex

From the vertex form, the vertex \((h,k)\) is \((-3,0)\).

Answer:

A. \((-3, 0)\)