[tex]B)y=2(x-2)^2+4[/tex]
1) Since the vertex is at (2,4) and there is another point, we can write out the following using the vertex quadratic form and those points:
[tex]\begin{gathered} y=a(x-h)^2+k \\ \\ 6=a(3-2)^2+4 \\ \\ 6=a+4 \\ \\ 6-4=a \\ a=2 \end{gathered}[/tex]
2) Now, that we know the coefficient "a" we can tell that this is the equation of that parabola by plugging a=2 into the vertex form:
[tex]y=2(x-2)^2+4[/tex]
And that is the answer.
