Question

How do you write the vertex form equation of each parabola given Vertex at origin, Focus (0, -1/32)?

Answer 1

`"The eqn. of Parabola is y"=-8x^2.` graph{-8x^2 [-10, 10, -5, 5]} #

Explanation:

Vertex and Focus of the parabola are, resp. `O(0,0) and S(0,-1/32)`.

Therefore, the Axis of the Parabola is the line joining `O and S`, i.e.,

the Y-axis.

Hence, the eqn. of the Parabola is of the form `: x^2=4by`.

But, then the Focus would be `S(0,b). :. b=-1/32`

So, the reqd. eqn. is `: x^2=4(-1/32)y, or, y=-8x^2.`