Question

suppose a parabola has an axis of symmetry at x=-8, a maximum height of 2, and passes through the point (-7,-1). write the equation of the parabola in vertex form

Answer 1

Its standard form of equation: (x-h)^2=-4p (y-k), (h,k)=(x,y) coordinates of the vertex
For given parabola: Vertex = (-8, 2)
(x-(-8))² = -4p(y - 2)

solve for 4p using coordinates of given point ( -7, -1)
-7+8  = 4p (-1 - 2)
1 = 4p(-3)
4p = -1/3

So, Equation of given parabola:
(x+8)² = -(y-2) / 3

Hope this helps!