Question

find the vertex, axis of symmetry, x - intercept, y - intercepts, focus, and directrix for the parabola
$x = - \frac { 1 } { 2 } y ^ { 2 }$. sketch the graph.
the vertex is $(0,0)$.
(simplify your answer. type an ordered pair.)
the axis of symmetry is
(simplify your answer. type an equation.)

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola of the form \(x = ay^{2}+by + c\) has its axis of symmetry given by \(y=-\frac{b}{2a}\). For the parabola \(x =-\frac{1}{2}y^{2}+0y + 0\), where \(a =-\frac{1}{2}\), \(b = 0\) and \(c = 0\).

Step2: Calculate the axis of symmetry

Using the formula \(y =-\frac{b}{2a}\), substitute \(a=-\frac{1}{2}\) and \(b = 0\). Then \(y=-\frac{0}{2\times(-\frac{1}{2})}=0\).

Answer:

The axis of symmetry is \(y = 0\)