Give Two Parametric Representations for the Equation of the Parabola $$y = ( x - 2 ) ^ { 2 } - 1$$

question 266

Multiple Choice

Give two parametric representations for the equation of the parabola.
- $$y = ( x - 2 ) ^ { 2 } - 1$$

• A) \(x = t , y = ( t + 2 ) ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty ) ; x = t + 2 , y = t ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty )\)
• B) \(x = t , y = ( t - 2 ) ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty ) ; x = t + 2 , y = t ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty )\)
• C) \(x = t , y = ( t - 2 ) ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty ) ; x = t - 2 , y = t ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty )\)
• D) \(x = t , y = ( t + 2 ) ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty )\); \(x = t - 2 , y = t ^ { 2 } - 1\) for \(t\) in \(( \infty , \infty )\)

---

Definitions:

Tilted Rocks

Rocks that have been moved from their original horizontal position to a slanted orientation, typically as a result of tectonic forces.

Angular Fragments

Sharp-edged pieces of rock or mineral that have not been significantly worn down by erosion, indicating little transport from their source.

Gray Layer

A sediment or rock layer characterized by its gray color, often indicating the presence of organic material or certain minerals.

Tilted Rocks

Rock formations that have been moved from their original position, usually as a result of tectonic activities, leaving them at an angle.