Write an equation of a parabola that has: 1. a y-intercept at (0,6), 2. a Vertex at (-1,a) and 3. a=2k

Answer 1

The vertex is at the point (-1, a) and a is 2k. So the vertex is at point (-1, 2k). The vertex of a parabola is (h,k) so h = -1 and k = 2k. If k = 2k then k = 0. So the vertex is at (-1, 0).

Vertex form of a parabola is y = A(x - h)² + k

So vertex form of this parabola is y = A(x+1)².

To find A, we'll use the last piece of information: a y-intercept at (0, 6)

Plug in (0,6) and solve for A.

(6) = A( (0)+1 )²

6 = A(1)²

6 = A

Therefore, the vertex form of the parabola is y = 6(x+1)²