Geometry

Question Analysis  

The main focus is to determine the domain and range of a horizontal parabola from its standard form equation.  

Key Concept Explanation  

Horizontal Parabola Form: The equation represents a horizontal parabola with vertex .  

Range: All real numbers () for horizontal parabolas (extends infinitely upward/downward).  

Domain: Depends on the direction of opening:  

If p > 0 (opens right), domain is .  

If p < 0 (opens left), domain is .  

Step-by-Step Solution  

1. Identify the parabola’s orientation and key parameters:  

Given , rewrite it as .  

Vertex: .  

(since p < 0, the parabola opens left).  

2. Determine the range:  

For any horizontal parabola, the range is all real numbers:  

.

3. Determine the domain:  

Since the parabola opens left (p < 0), the domain starts at the

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