Give Two Parametric Representations for the Equation of the Parabola $$y = x ^ { 2 } + 6 x + 15$$

question 270

Multiple Choice

Give two parametric representations for the equation of the parabola.
- $$y = x ^ { 2 } + 6 x + 15$$

• A) \(x = t , y = t ^ { 2 } + 6 t + 15\) for \(t\) in \(( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } + 6\) for \(t\) in \(( \infty , \infty )\)
• B) \(x = t , y = t ^ { 2 } - 6 t - 15\) for \(t\) in \(( \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 6\) for \(t\) in \(( \infty , \infty )\)
• C) \(x = t , y = t ^ { 2 } + 6 t + 15\) for \(t\) in \(( \infty , \infty ) ; x = t + 3 , y = t ^ { 2 } + 6\) for \(t\) in \(( \infty , \infty )\)
• D) \(x = t , y = t ^ { 2 } + 6 t + 15\) for \(t\) in \(( \infty , \infty ) ; x = t - 3 , y = t ^ { 2 } - 6\) for \(t\) in \(( \infty , \infty )\)

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Definitions:

Fixed Interval

A type of reinforcement schedule in operant conditioning where rewards are provided after a specific, constant amount of time has passed.

Fixed Ratio

Fixed ratio denotes a schedule of reinforcement where a response is reinforced only after a specified number of responses have occurred.

Variable-interval Schedule

A schedule of reinforcement where a response is rewarded after an unpredictable amount of time has passed, contributing to a steady, stable rate of response.

Specific Number

An exact quantity or value, often mentioned to denote precision or to highlight importance within a particular context.