Question

Find the point on the parabola x+y^2=0 that is closest to the point (o,-3)

Answer 1

So just by looking at it you can tell that the vertex is \((0, 0)\).

Answer 2

We also know it opens up to the left or right, because it is horizontal.

Answer 3

Getting it in standard parabola form \(y^2 = 4px\) we get: \[
y^2 = 4\left(-\frac{1}{4}\right)x
\]This means the focus is at \((-1/4, 0)\) and the directrix is \(x=1/4\)