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 + 10)²
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use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.
click to enlarge graph

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 and the axis of symmetry is \( x = h \).

Step2: Rewrite given function

Given \( h(x) = (x + 10)^2 \), we can rewrite it as \( h(x) = 1(x - (-10))^2 + 0 \).

Step3: Identify vertex and axis

From the vertex form, \( h = -10 \) and \( k = 0 \), so the vertex is \((-10, 0)\). The axis of symmetry is \( x = -10 \).

Answer:

Vertex: \((-10, 0)\), Axis of Symmetry: \( x = -10 \)