ed9c9a…: “Within a stormy flower”

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Suppose that we want to give a vector-valued function that traces out the curve described by $x=4y^2+7y-1$ .

By requiring that $y(t) = 4t$ , find the position vector that traces out this curve.

$\vec {p}(t) = \vector {\answer {64t^2+28t-1},\answer {4t}}.$

The point on the curve where $y=1$ is $(x,y) = \left (\answer {10},1\right )$ . At what time $t$ is this point drawn?

$t = \answer {\frac {1}{4}}$