SOLUTION
The vertex form of a quadratic equation is:
[tex]y=a(x-h)^2+k[/tex]
The given vertex is (1,2)
It follows h = 1, k = 2
Substitute the values into the vertex equation
[tex]y=a(x-1)+2[/tex]
Since the line passes through (3,10) substitute x=3 and y=10 into the equation
This gives
[tex]10=a(3-1)^2+2[/tex]
Solve for a
[tex]\begin{gathered} 10=a(2)^2+2 \\ 10=4a+2 \\ 8=4a \\ a=2 \end{gathered}[/tex]
Substitute the value of a into the vertex form equation
[tex]y=2(x-1)^2+2[/tex]
The required equation is:
[tex]y=2(x-1)^{2}+2[/tex]
