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A parametric function is given by the coordinates . Eliminate the parameter to find an equivalent function y in terms of x.

A parametric function is given by the coordinates . Eliminate the parameter to find-example-1
User Steven Van Ingelgem
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1 Answer

20 votes
20 votes

Solution:

Given:


\begin{gathered} Coordinates: \\ (5-t,t^2+4t-1) \end{gathered}

This implies that:


\begin{gathered} x=5-t \\ y=t^2+4t-1 \end{gathered}

Using the coordinate x,


\begin{gathered} x=5-t \\ Making\text{ t the subject of the formula;} \\ t=5-x \end{gathered}

Hence, substituting t into coordinate y,


\begin{gathered} y=t^2+4t-1 \\ y=(5-x)^2+4(5-x)-1 \\ Expanding\text{ the brackets;} \\ y=25-10x+x^2+20-4x-1 \\ Collecting\text{ the like terms together and simplfying;} \\ y=25+20-1-10x-4x+x^2 \\ y=44-14x+x^2 \\ \\ Rearranging\text{ the terms:} \\ y=x^2-14x+44 \end{gathered}

Therefore,


y=x^2-14x+44

User DeeDub
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