PARAMETRIC 2020-21 U11 Parametric Functions

What is the first step in converting from parametric to rectangular?

• Solve one of the equations for x

• Solve one of the equations for y

• Solve one of the equations for t

• Substitute one equation into the other

What is the second step in converting from parametric to rectangular?

• Simplify the x-equation

• Substitute the expression for t in the other equation

• Solve for t

• Substitute the expression for x in the other equation

 $x=t^2-6t+3$  
 $y=6-2t$  

 $0\le t\le6.28$  

Which is the graph of the parametric function?

• 
• 
• 
• 

 $x=4+t$  
 $y=2t+1$  
Write the rectangular equation for the parametric equations.  $0\le t\le6.28$  

•  $y=-2x+9$ 

•  $y=2x+9$ 

•  $y=2x-7$  

•  $y=-x+4$ 

 $x=4-3t$  
 $y=-3+2t$   $0\le t\le6.28$  
What is the rectangular form of this equation?

• $y=\frac{2}{3}x+\frac{1}{3}$

• $y=-\frac{2}{3}x+\frac{1}{3}$

• $y=\frac{2}{3}x+\frac{8}{3}$

• $y=-\frac{2}{3}x-\frac{1}{3}$

The graph given by these functions will cross the x-axis at what point? 
 $x=t^3+5$  
 $y=-4+2t$  
 $0\le t\le3$  

•  $\left(11,0\right)$  

•  $\left(0,13\right)$  

•  $\left(5,0\right)$  

•  $\left(13,0\right)$  

The graph given by these functions will cross the y-axis at what point(s)? 

 $x=t^2+4t$  
 $y=-7-t$  
 $-5\le t\le5$  

•  $\left(-7,0\right)\ and\ \left(-3,0\right)$  

•  $\left(0,-7\right)$  

•  $\left(0,-7\right)\ and\ \left(0,-3\right)$  

•  $\left(0,-7\right)\ and\ \left(0,-11\right)$  

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

• eliminating
• finding
• converting
• jumping

Convert from parametric to rectangular
 $x=t-4$  

 $y=2t+1$  
 $-10\le t\le10$  

• y = 2t - 4

• y = 2x + 9

• y = 2x + 4

• y = 2t - 3

An NFL punter at the 20 yard line kicks a football downfield with an initial velocity of 75 ft/sec at an angle of 66⁰. The ball leaves his foot at a height of 3 feet.

Model the scenario using parametric equations.

• x = 20cos(66)t;

  y =20sin(66)t -16t² + 75

• x = 20cos(66)t;

  y = 20sin(66)t -4.9t² + 3

• x = 75cos(66)t;

  y = 75sin(66)t -16t² + 20

• x = 75cos(66)t;

  y = 75sin(66)t -16t² + 3