Geometry

Question Analysis  

The main focus is to determine the equation of a parabola using the vertex form, verify its orientation with a given point, and identify its domain and range based on whether it is vertical or horizontal.  

Key Concept Explanation  

Vertex Form:  

Vertical: (opens up/down, -squared term).  

Horizontal: (opens left/right, -squared term).  

Domain/Range:  

Vertical: Domain = all real numbers (), Range depends on and .  

Horizontal: Range = , Domain depends on and .  

Step-by-Step Solution  

1. Test vertical parabola form:  

Vertical equation: .  

Substitute point :  

.

2. Use horizontal parabola form:  

Horizontal equation: (since , vertex ).  

Substitute point :  

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