Question

1. which of the following statements describe the function below? select all that apply.

$y=2(x-3)^2+7$

• the vertex of the function is a maximum.
• the vertex of the function is (3,7).
• the vertex of the function is a minimum.
• the vertex of the function is (2,−3).

Explanation:

1. For a quadratic function in vertex form \(y = a(x - h)^2 + k\), the vertex is \((h, k)\). Here, \(h = 3\) and \(k = 7\), so the vertex is \((3, 7)\).
2. The coefficient \(a = 2\) (positive), so the parabola opens upward. An upward - opening parabola has its vertex as the minimum point.

Answer:

The vertex of the function is \((3,7)\).
The vertex of the function is a minimum.