Write the quadratic function given: vertex @ (4, 2) and a point of (0, 8)

Answer 1

Hi Faith! If you've been given a vertex, the standard quadratic function looks like this:

y = a*(x-h)^2 + k

where (h,k) is the vertex - in our case, h = 4, k = 2. So that gives us:

y = a*(x-4)^2 + 2

We still need to know a, but we have a second point: (0,8). Let's plug in:

8 = a*(0-4)^2 + 2

8 = a*(-4)^2 + 2

8 = a*16 + 2

6 = a*16

a = 6/16 = 3/8

So our formula is:

y = 3/8*(x-4)^2 + 2

Answer 2

a standard upward opening parabola would have general form

y-h = a(x-k)^2 where (k,h) is the vertex, plug the vertex in to get

y-2=a(x-4)^2, then plug the point in to solve for a

8-2 =a(-4)^2 = 16a

a= 6/16 = 3/8

the quadratic is

y-2 =(3/8)(x-4)^2