The line below has two points which correspond to values of a parameter $t.$

Write the parametric equations for this line, using $t$ for the parameter.

$[$Each equation should be a linear function of $t.]$

$x=f(t)=$

$y=g(t)=$

What point on the line would correspond to $t=10?$

Answer: $q,$

Let $x=3t^2,y=-2t^{2}18t.$

Determine $\frac{dy}{dx}$ as a function of $t,$ then find the slope of the parametric curve at $t=4\mathrm{.}5.$

$\frac{dy}{dx}=$

$\frac{dy}{dx}(4\mathrm{.}5)=$

Determine $\frac{d^{2}y}{d{x}^2}$ as a function of $t,$ then find the concavity of the parametric curve at $t=4\mathrm{.}5.$

$($Hint: The Second Derivative Test for Extrema could help.$)$

$\frac{d^{2}y}{d{x}^2}=$

$\frac{d^{2}y}{d{x}^2}(4\mathrm{.}5)=$

The position of an object at time $t$ is given by the parametric equations $x=3t^{2}1t$

$y=4t^{2}5.$

Find the velocity and speed at the moment where $t=3.$

Velocity $=$

Speed $=$

Sketch a graph of $x=t-3,y=t2.$