Question

write an equation for a parabola with a vertex at (0,0) and a focus at (0, -4).
be sure not to add any spaces or decimals in your response.
$x^{2}=$

Explanation:

Step1: Determine the form of the parabola equation

Since the vertex is \((0,0)\) and the focus is \((0, - 4)\), the parabola opens downwards. The standard form of a parabola that opens up or down is \(x^{2}=4py\), where \((0,p)\) is the focus.

Step2: Find the value of \(p\)

Given the focus \((0,-4)\), we have \(p=-4\).

Step3: Substitute \(p\) into the standard form

Substitute \(p = - 4\) into \(x^{2}=4py\). We get \(x^{2}=4\times(-4)y\).

Answer:

\(x^{2}=-16y\)