How do you write the equation of the parabola in vertex form given vertex (0,0) and the directrix y=-16?

Jul 2, 2017

$y = \frac{1}{64} {x}^{2}$

Explanation:

Given -

Vertex $\left(0 , 0\right)$
Directrix $\left(y = - 16\right)$
Focus $\left(0 , 16\right)$

The Parabola is opening up, as its directrix is $y = - 16$

The formula for the parabola in the vertex form is -

${\left(x - h\right)}^{2} = 4. a . {\left(y - k\right)}^{2}$

Where -

$h = 0$ x-coordinate of the vertex
$k = 0$ y-coordinate of the vertex
$a = 16$ distance between vertex and focus

x-0)^2=4xx16(y-0)
${x}^{2} = 64 y$
$y = \frac{1}{64} {x}^{2}$