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 \\)symmetry as a dashed line.\
what is the vertex of the graph?\
the vertex is \\( (-2,1) \\).\
(type an ordered pair.)\
what is the equation for the axis of symmetry?\
\\( \square \\) (type an equation.)

Explanation:

Step1: Recall the vertex form of a quadratic function

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

Step2: Identify \( h \) from the given function

For the function \( h(x) = (x + 2)^2 + 1 \), we can rewrite it as \( h(x) = (x - (-2))^2 + 1 \). Comparing with \( y = a(x - h)^2 + k \), we see that \( h = -2 \) and \( k = 1 \).

Step3: Determine the axis of symmetry

Using the formula for the axis of symmetry from the vertex form, which is \( x = h \), substituting \( h = -2 \), we get the equation of the axis of symmetry as \( x = -2 \).

Answer:

The equation for the axis of symmetry is \( x = -2 \).