Parametric Equations

The variable "t" is called a

• parameter

• parallel

• paralegal

• paradise

Converting parametric equations to a rectangular equation is called _________________ the parameter.

• eliminating
• finding
• converting
• jumping

Which set of parametric equations satisfies the given data table?

• x(t) = t³ - 1
  y(t) = 2t
• x(t) = t³ - 1
  y(t) = t + 2
• x(t) = t + 8
  y(t) = t + 2
• x(t) = t + 8
  y(t) = 2t

Find the ordered pair based on the parametric equations.

t = -2

x = t² - 2

y = -t + 2

• (2, 4)

• (4, 2)

• (-6, 0)

• (0,-6)

Find the ordered pair based on the parametric equations when t=0

x(t) = e^t - e^-t

y(t) = e^t + e^-t

• (0, 2)

• (2.35, 3.08)

• (7.25, 7.52)

• (0, 0)

Find the ordered pair based on the parametric equations. t = 3

x = 1 - 2t

y =4t + 1

• (-5, 13)

• (13, -5)

• (5, 13)

• (13, 5)

Determine an appropriate set of parametric equations and window for the rectangular equation  $y=\left|2x+3\right|,\ 0\le x\le4$  

•  $x=\frac{t}{2},\ y=\left|t+\ 3\right|,\ 0\le t\le8$  

•  $x=\frac{t}{2},\ y=\left|t+3\right|,\ 0\le t\le2$  

•  $x=t,\ y=\left|t+3\right|,\ 0\le t\le4$  

•  $x=2t,\ y\ =\left|\frac{t}{2}+3\right|,\ 0\ \le t\le2$  

Write the rectangular equation for the following parametric equations.

x = 4cosθ

y = 3sinθ^

• $\frac{x^2}{9}+\frac{y^2}{16}=1$

• $\frac{y^2}{9}+\frac{x^2}{16}=1$

• $\cos^2\theta+\sin^2\theta=1$

• $\frac{x^2}{9}-\frac{y^2}{16}=1$

Write x = 2t  and y = t² + 3  in rectangular form .

• y = 4x²  + 3
• y = ¼ x² + 3
• y = 4t² + 12
• y = (x - 2)² + 3