How do you write the cartesian equation for x = t - 2 and y = -(t²) + t + 1?

Answer 1

Cartesian equation for given parametric equation is #x^2+3x+y+1=0#, which is the equation of a parabola.

As #x=t-2#, we have #t=x+2#
Hence #y=-t^2+t+1# can be written as #y=-(x+2)^2+x+2+1#
or #y=-x^2-4x-4+x+2+1#
or #x^2+3x+y+1=0#, which is the equation of a parabola.

graph{x^2+3x+y+1=0 [-10, 10, -5, 5]}

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Answer 2

To write the Cartesian equation for the given parametric equations ( x = t - 2 ) and ( y = -(t^2) + t + 1 ), eliminate the parameter ( t ) by isolating ( t ) in one of the equations and then substituting it into the other equation.

From the first equation: [ x = t - 2 ] [ t = x + 2 ]

Substitute ( t = x + 2 ) into the second equation: [ y = -(x + 2)^2 + (x + 2) + 1 ]

Now expand and simplify to obtain the Cartesian equation.

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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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