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.\\( f(x) = -(x - 2)^2 \\)\\( \dots \\)use the graphing tool to graph the function as a solid curve and the axis of symmetry as a dashed line.\\( \text{click to enlarge graph} \\)what is the vertex of the graph?the vertex is \\( \square \\)\\( \text{(type an ordered pair)} \\)what is the equation of the axis of symmetry?\\( \square \\)\\( \text{(type an equation.)} \\)

Explanation:

Step1: Recall vertex form of quadratic

The vertex form of a quadratic function is \( f(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.
For \( f(x) = -(x - 2)^2 \), we can rewrite it as \( f(x) = -1(x - 2)^2 + 0 \).

Step2: Identify vertex coordinates

Comparing with \( a(x - h)^2 + k \), we have \( h = 2 \) and \( k = 0 \). So the vertex is \((2, 0)\).

Step3: Determine axis of symmetry

The axis of symmetry for a quadratic in vertex form \( f(x) = a(x - h)^2 + k \) is the vertical line \( x = h \). Here, \( h = 2 \), so the axis of symmetry is \( x = 2 \).

Answer:

The vertex is \((2, 0)\). The equation of the axis of symmetry is \( x = 2 \).