Question

match the function with its graph.
$g(x)=(x + 4)^2$

Explanation:

Step1: Analyze the function form

The function \( g(x)=(x + 4)^2 \) is a quadratic function in the form \( y=a(x - h)^2+k \), where \( a = 1\), \( h=- 4\), \( k = 0\). For a quadratic function \( y=a(x - h)^2+k \), the vertex is at \((h,k)\), so the vertex of \( g(x)\) is at \((-4,0)\). Also, since \( a=1>0 \), the parabola opens upwards.

Step2: Match with the graphs

We look for a parabola that opens upwards (so we can eliminate the ones opening downwards like A, H) and has its vertex at \((-4,0)\). Checking the graphs, graph B has its vertex at \((-4,0)\) and opens upwards.

Answer:

B