The problem asks to plot the vertex and the axis of symmetry for the function $f(x) = (x - 3)^2 + 5$. Let’s break this down:

1. Vertex:

The function is written in vertex form: $f(x) = a(x-h)^2 + k$, where:

• $h$ is the x-coordinate of the vertex.
• $k$ is the y-coordinate of the vertex.

Here:

• $h = 3$
• $k = 5$

So, the vertex is at $(3, 5)$.

2. Axis of Symmetry:

The axis of symmetry is a vertical line that passes through the x-coordinate of the vertex:

• Equation: $x = 3$.

Steps for Plotting:

1. Mark the vertex at $(3, 5)$ on the graph.
2. Draw a vertical line at $x = 3$ to represent the axis of symmetry.

Would you like additional help with the graph or further explanation?

Related Questions:

1. How does the vertex form of a quadratic function help identify key graph features?
2. What is the significance of the axis of symmetry in quadratic functions?
3. How would the graph change if the function was $f(x) = -(x - 3)^2 + 5$?
4. Can you derive the standard form of the function $f(x) = (x - 3)^2 + 5$?
5. How does the value of $a$ in the vertex form $f(x) = a(x-h)^2 + k$ affect the graph's shape?

Tip:

Always check the vertex form to immediately identify the vertex and symmetry, saving time when graphing!