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
(simplify your answer. type an ordered pair.)

Explanation:

Step1: Recall the standard form of a parabola

The standard form of a parabola that opens left - right is \((y - k)^2=4p(x - h)\), where \((h,k)\) is the vertex.
For the given equation \(x =-\frac{1}{2}y^{2}\), we can rewrite it as \((y - 0)^2=-2(x - 0)\)

Step2: Identify the vertex

Comparing with the standard form \((y - k)^2 = 4p(x - h)\), when \(h = 0\) and \(k=0\), the vertex \((h,k)=(0,0)\)

Answer:

\((0,0)\)