Question

find the vertex and the axis of symmetry of the graph of $f(x) = 3(x - 3)^2 + 6$. the vertex is $(square, square)$. the axis of symmetry is $x = square$.

Explanation:

Step1: Recall vertex form of parabola

The vertex form of a parabola is \( f(x)=a(x - h)^2 + k \), where \((h,k)\) is the vertex and the axis of symmetry is \( x = h \).

Step2: Identify \( h \) and \( k \) from given function

For the function \( f(x)=3(x - 3)^2 + 6 \), comparing with \( f(x)=a(x - h)^2 + k \), we have \( h = 3 \) and \( k = 6 \).

Step3: Determine vertex and axis of symmetry

So the vertex is \((h,k)=(3,6)\) and the axis of symmetry is \( x = h = 3 \).

Answer:

The vertex is \((3,6)\). The axis of symmetry is \( x = 3 \).