Question

Write an equation for a function that has the given graph. The bottom half of the parabola \(x+y^{2}=0\)

Short answer

The equation of the bottom half of the parabola \(x+y^{2}=0\) is \(y=-\sqrt{-x}\)

Step-by-step solution

Identify the function

The equation provided \(x+y^{2}=0\) is a parabola when rearranged to \(y=\sqrt{-x}\). However, this equation represents both halves of the parabola, and we're only interested in the bottom half.

Solve for the bottom half

In order to isolate the bottom half of the parabola, we must represent the \(y=\sqrt{-x}\) function in a manner that only yields negative y-values. We know that the square root of a number is always positive, hence, if we take the negative of this square root, we will get the bottom half of the parabola. Therefore, \(y=-\sqrt{-x}\) represents the bottom half of the parabola.