Question

determine the equation in standard form of the parabola that satisfies the given conditions
focus at (0, -3); vertex at (0, 0)
question help: video ebook

Explanation:

Step1: Identify the form of the parabola

Since the vertex is \((0,0)\) and the focus is \((0, - 3)\), 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: Determine the value of \(p\)

Given the focus \((0,-3)\), we have \(p=-3\).

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

Substitute \(p = - 3\) into \(x^{2}=4py\). We get \(x^{2}=4\times(-3)y\).

Answer:

\(x^{2}=-12y\)