Given vertex [tex](h,k)[/tex] the equation of the parabola is:
[tex]f(x)=a(x-h)^2+k[/tex].
Our vertex is the point [tex](3,5)[/tex] so the equation is:
[tex]f(x)=a(x-3)^2+5[/tex]. It remains to find a. We will use the point (1,-3) like
this:
Substitute x=1 and f(1)=-3 in the equation above we get the equation:
[tex]-3=a(1-3)+5\\-3=-2a+5\\-2a=-8\\a=4[/tex]
Equation of the parabola then: [tex]f(x)=4(x-3)^2+5[/tex].
Expand in order to get the general form:
[tex]f(x)=4(x^2-3x+9)+5\\y=4x^2-12x+41[/tex]
