Geometry

Question Analysis  

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

Key Concept Explanation  

Vertical Parabola Form: The equation represents a vertical parabola with vertex .  

Domain: All real numbers () for vertical parabolas (extends infinitely left/right).  

Range: Depends on the direction of opening:  

If p > 0(opens upward), range is .  

 If p < 0 (opens downward), range 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 upward).  

2. Determine the domain:  

For any vertical parabola, the domain is all real numbers:  

.

3. Determine the range:  

Since the parabola opens upward (p > 0), the range starts at the

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