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Give a parametric representation of the parabola y = (x+7)^2 -5

User Derfder
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We have to find the parametric representation of the parabola y = (x+7)² - 5, which is represented in vertex form.

Parametric representations use a third variable on which we define x and y.

We will call this variable t.

We can start with defining t as:


\begin{gathered} t=x+7 \\ \Rightarrow x(t)=t-7 \end{gathered}

We then have already x in function of t.

Then, we can use the definition of t to find y(t):


\begin{gathered} y(t)=(x(t)+7)^2-5 \\ y(t)=(t-7+7)^2-5 \\ y(t)=t^2-5 \end{gathered}

We then have x and y defined in function of t.

Answer: we can represent the parabola in a parametric form as

x(t) = t-7

y(t) = t² - 5

User Ted Fitzpatrick
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