Question

sketch the graph of the quadratic function and the axis of symmetry. state the vertex, and give the equation for the axis of symmetry.\\( h(x) = (x + 2)^2 + 1 \\)\\( \dots \\)use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.\
what is the vertex of the graph?\
the vertex is \\( \square \\).\
(type an ordered pair.)

Explanation:

Step1: Recall vertex form of quadratic

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

Step2: Compare with given function

Given \( h(x) = (x + 2)^2 + 1 \), rewrite \( x + 2 \) as \( x - (-2) \). So, \( a = 1 \), \( h = -2 \), \( k = 1 \).

Step3: Identify vertex

From the vertex form, the vertex \((h, k)\) is \((-2, 1)\).

Answer:

\((-2, 1)\)