Answer:
y=(x-1)²+4
Step-by-step explanation:
The equation for a parabola in vertex form is y=a(x-h)²+k
(h,k) represents the vertex of the parabola
The value of "a" represents the stretch or compression factor
Since the vertex is (1,4) this means (h,k)=(1,4). To find the value of a, we plug in (3,8) as (x,y) in the equation:
y=a(x-h)²+k
8=a(3-1)²+4
8=a(2)²+4
8=a(4)+4
8=4a+4
4=4a
a=1
Since a=1 the parabola doesn't compress or stretch. This means that our final equation is y=(x-1)²+4
