Question

Find the equation for the parabola with vertex (1,4) that passes through the point (3,8)

Answer 1

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