What is the axis of symmetry and vertex for the function $f(x)=3(x-2)^{2}+4$ ? $x=6$
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Answer

$\boxed{\text{The vertex of the function }f(x)=3(x-2)^{2}+4\text{ is }(2,4)\text{ and the axis of symmetry is }x=2}$

Steps

Step 1 ：The function given is $f(x)=3(x-2)^{2}+4$

Step 2 ：The vertex form of a parabola is $f(x)=a(x-h)^{2}+k$, where $(h,k)$ is the vertex

Step 3 ：Comparing this with the given function, we can see that $h=2$ and $k=4$

Step 4 ：So, the vertex of the function is $(2,4)$

Step 5 ：The axis of symmetry for a parabola in vertex form is $x=h$

Step 6 ：So, the axis of symmetry for this function is $x=2$

Step 7 ：$\boxed{\text{The vertex of the function }f(x)=3(x-2)^{2}+4\text{ is }(2,4)\text{ and the axis of symmetry is }x=2}$