How do you convert parametric equation to cartesian x = t - 2 and y = -(t²) + t + 1?

Answer 1

#y= - x^2 - 3x -1#

separate out the #t# term
#x = t - 2 implies t = x + 2#

sub that into the other equation

#y = - t^2 + t + 1 #
#= - (x + 2)^2 + (x+2) + 1#
#= - (x^2 + 4x + 4) + x+3#
#implies y= - x^2 - 3x -1#
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Answer 2

To convert parametric equations to Cartesian equations, you simply solve one equation for ( t ) and substitute it into the other equation.

Given the parametric equations:

[ x = t - 2 ] [ y = -(t^2) + t + 1 ]

We can solve the first equation for ( t ):

[ t = x + 2 ]

Now, substitute this expression for ( t ) into the second equation:

[ y = -((x + 2)^2) + (x + 2) + 1 ]

Expanding and simplifying:

[ y = -(x^2 + 4x + 4) + x + 2 + 1 ] [ y = -x^2 - 4x - 4 + x + 2 + 1 ] [ y = -x^2 - 3x - 1 ]

So, the Cartesian equation equivalent to the given parametric equations is:

[ y = -x^2 - 3x - 1 ]

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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