For this quadratic, its vertex form [tex]f(x) = a(x-h)^2+k[/tex] is [tex]f(x) = a(x-1)^2+3[/tex].
To find the value of a, plug in (0,5) and solve.
[tex]5 = a(0-1)^2+3 \\ a = 2[/tex]
The final equation in vertex form is [tex]f(x) = 2(x-1)^2+3[/tex].
In standard form [tex]f(x) = ax^2+bx+c[/tex], the function is [tex]f(x) = 2x^2-4x+5[/tex].
