Question

use the information provided to write the vertex form equation of each parabola. 4) vertex at origin, focus: (0, -1)

Explanation:

Step1: Recall the vertex form of a parabola

For a parabola that opens up or down, the vertex form is \(x^{2}=4py\), where \((0, p)\) is the focus and the vertex is at \((0,0)\).

Step2: Determine the value of \(p\)

The focus is given as \((0, - 1)\), so comparing with \((0,p)\), we have \(p=-1\).

Step3: Substitute \(p\) into the equation

Substitute \(p = - 1\) into the equation \(x^{2}=4py\). We get \(x^{2}=4\times(-1)y\), which simplifies to \(x^{2}=-4y\).

Answer:

The vertex form equation of the parabola is \(x^{2}=-4y\)