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

Sep 29, 2016

Answer:

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

Explanation:

Vertex and Focus of the parabola are, resp. $O \left(0 , 0\right) \mathmr{and} S \left(0 , - \frac{1}{32}\right)$.

Therefore, the Axis of the Parabola is the line joining $O \mathmr{and} S$, i.e.,

the Y-axis.

Hence, the eqn. of the Parabola is of the form $: {x}^{2} = 4 b y$.

But, then the Focus would be $S \left(0 , b\right) . \therefore b = - \frac{1}{32}$

So, the reqd. eqn. is $: {x}^{2} = 4 \left(- \frac{1}{32}\right) y , \mathmr{and} , y = - 8 {x}^{2.}$