Use the drawing tool(s) to form the correct answer on the provided graph.

Question

Plot the axis of symmetry and the vertex for this function:

h(x) = (x − 5)2 − 7.

Answer 1

To plot the axis of symmetry and the vertex for the function \( h(x) = (x - 5)^2 - 7 \), follow these steps:

1. Identify the vertex: The function is in vertex form, \( h(x) = a(x - h)^2 + k \), where \((h, k)\) is the vertex.

   • Here, \( h = 5 \) and \( k = -7 \). Thus, the vertex is \((5, -7)\).

2. Find the axis of symmetry: The axis of symmetry for a quadratic function in vertex form is the vertical line passing through the vertex.

   • Since the x-coordinate of the vertex is 5, the equation of the axis of symmetry is \( x = 5 \).

Now, you can plot the vertex at the point \((5, -7)\) on the graph and draw the line \( x = 5 \) to represent the axis of symmetry.

If you have graphing tools or tools to draw, you can perform these actions accordingly!