Question

what is the vertex of the quadratic function
\\f(x) = 2(x - 3)^2 + 1?\\

\\(\bigcirc\\) \\((3, 1)\\)
\\(\bigcirc\\) \\((3, -1)\\)
\\(\bigcirc\\) \\((-3, 1)\\)
\\(\bigcirc\\) \\((2, 1)\\)

Explanation:

⚡ Using what you learned: vertex and axis of symmetry

Step 1: Identify the form of the quadratic function

The given function is:

$$ f(x) = 2(x - 3)^2 + 1 $$

This is written in vertex form:

$$ f(x) = a(x - h)^2 + k $$

Step 2: Extract the vertex coordinates

By comparing the equations:

• \( h = 3 \)
• \( k = 1 \)

The vertex is \( (h, k) \):

$$ (3, 1) $$

Answer:

\( (3, 1) \)