Question

Find the standard form of the equation of the parabola with a vertex at the origin and a focus at (0, -7).

Answer 1

so hmmm notice the picture below

we know the vertex is at the origin, and the focus at 0,-7

now, notice the distance "p", which is the distance between the vertex and focus or directrix

based on the given points, we know the parabola is vertical, and opening downwards, thus, the squared variable is the "x"

thus
`\bf \begin{array}{llll} (y-{{ k}})^2=4{{ p}}(x-{{ h}}) \\\\ \boxed{(x-{{ h}})^2=4{{ p}}(y-{{ k}})}\\ \end{array} \qquad \begin{array}{llll} vertex\ ({{ h}},{{ k}})\\\\ {{ p}}=\textit{distance from vertex to }\\ \qquad \textit{ focus or directrix} \end{array}`

plug in the values for it then