Question

which is the axis of symmetry of a parabola with equation $x^2 = -4y$?
$x = -4$
$x = -1$
$x = 1$
$x = 0$

Explanation:

Step1: Recall parabola standard form

The standard form of a parabola that opens up or down is \(x^{2}=4py\) (opens up if \(p>0\), down if \(p < 0\)). The axis of symmetry for this form is \(x = 0\) (the \(y\)-axis), since the equation is symmetric about the line where \(x=0\) (replacing \(x\) with \(-x\) gives the same equation: \((-x)^{2}=4py\Rightarrow x^{2}=4py\)).

Step2: Analyze given equation

The given equation is \(x^{2}=- 4y\), which is in the form \(x^{2}=4py\) with \(p=-1\). Using the symmetry property of this parabola form, the axis of symmetry is \(x = 0\).

Answer:

\(x = 0\)