Question

choose the graph of $y = (x - 3)^2 + 1$.

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( y = a(x - h)^2 + k \), where \((h, k)\) is the vertex. For \( y=(x - 3)^2+1 \), the vertex is \((3, 1)\).

Step2: Analyze the graphs

• First graph: Vertex seems around \((2, 0)\), not \((3, 1)\).
• Second graph: Vertex is left of y - axis, not \((3, 1)\).
• Third graph: Vertex is around \((3, 1)\) (x = 3, y = 1 approximately on the grid), and it opens upwards (since \(a = 1>0\)), matching the parabola \( y=(x - 3)^2+1 \).

Answer:

The Right Graph