Answer:
B. y=3(x-1)2 + 3
Step-by-step explanation:
Given that
vertex of the parabola is at the point (1,3)
let's verify, if the option B is the correct equation of the parabola.
[tex]y=3(x-1)^2 + 3\\ \\y=3(x^2+1-2x) + 3\\\\y=3x^2+3-6x + 3\\\\y=3x^2-6x + 6....Eq1[/tex]
comparing to standard equationof parabola (standard quadratic equation), we get
[tex]a=3, b=-6 and c=6[/tex]
to find the vertex we use formula for x- coordinate as [tex]x=-b/2a[/tex]
[tex]x=-(-6)/2(3)\\\\x=6/6\\x=1[/tex]
to find y put x=1 in the Eq1, we get
[tex]y=3(1)^2-6(1)+6\\\\y=3-6+6\\\\y=3[/tex]
vertex =(x,y) = (1, 3)
thus vertex of the parabola from the equation y=3(x-1)2 + 3 is (1,3), thus verified
