Question

How do you write the equation of each parabola in vertex form given vertex at (0,4) and passes through the point (-1,6)?

Answer 1

`y=2x^2+4`

Explanation:

`y=a(x-h)^2+k` => equation of the parabola in vertex form where:
(h, k) is the coordinates of the vertex.
So in this case we substitute the given coordinates in the formula:
`y=a(x-0)^2+4` => simplify:
`y=ax^2+4` => to solve for a we substitute the given coordinates:
`6=a*(-1)^2+4` => simplify:
`6=a+4` => solve for a
`6-4=a` => or:
`a=2` => substitute for a and the required equation is:
`y=2x^2+4`