Geometry

Question Analysis  

The main focus is to identify the vertex, focus, and directrix of a horizontal parabola from its standard form equation.  

Key Concept Explanation  

Standard Form of a Horizontal Parabola: The equation represents a horizontal parabola with:  

Vertex: .  

Focus: if p > 0 (opens right) or if p < 0 (opens left).  

Directrix: (vertical line).  

The sign of determines the direction: p > 0 (right), p < 0 (left).  

Step-by-Step Solution  

1. Rewrite the equation in standard form:  

Given , compare to :  

.

2. Determine key features:  

Vertex: (always the origin for ).  

Focus: Since (negative), the parabola opens left, and the focus is at .  

Directrix:

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