Geometry

Question Analysis  

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

Key Concept Explanation  

Standard Form of a Vertical Parabola: The equation represents a vertical parabola with:  

Vertex: .  

Focus: if p > 0 (opens upward) or if p < 0 (opens downward).  

Directrix: (horizontal line).  

The sign of determines the direction: p > 0 (upward), p < 0 (downward).  

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 downward, and the focus is at .  

Directrix: .  

Common Mistakes  

Misinterpreting the sign of : Forgetting that a negative coefficient in

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