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I need help with this practice problem solving The subject is parametric equations

I Need Help With This Practice Problem Solving The Subject Is Parametric Equations class=

Sagot :

Solution

Given the following parametric equation

[tex]x(t)=t-3,y(t)=2t^2-1[/tex]

To find the rectangular form of the given parametric equations, make x the subject as shown below

[tex]\begin{gathered} x=t-3 \\ t=x+3 \end{gathered}[/tex]

Substitute for t into y(t),

[tex]\begin{gathered} y=2(x+3)^2-1 \\ y=2(x(x+3)+3(x+3))-1 \\ y=2(x^2+3x+3x+9)-1 \\ y=2(x^2+6x+9)-1 \\ y=2x^2+12x+18-1 \\ y=2x^2+12x+17 \end{gathered}[/tex]

For the interval of x, where t = -2

[tex]x=-2-3=-5[/tex]

Where t = 2

[tex]x=2-3=-1[/tex]

Hence, the answer is

[tex]y=2x^2+12x+17\text{ where x ix on the interval }(-5,-1)[/tex]

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