ShmoopTube

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Here's your shmoop du jour, brought to you by parametric equations.

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Which have nothing to do with EMTs, ambulances or blood transfusions you read about.

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Thank goodness.

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If x = t + 1 and y = 3t squared + 2t - 1,

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then y is also equal to which of the following?

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And here are the potential answers...

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See those t's in the x and y equations?

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This shows us that we're dealing with something

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called PARAMETRIC equations.

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It's basically where we write our x and y equations in terms of another variable...like t.

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This question asks us to solve for y...if we look at our answer choices, they want us

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to solve for y in terms of x.

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Well, we can do this by solving for t in terms of x and then substituting

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the t value in terms of x back into the y equation.

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Rearranging the first equation so that  t is by itself on one side...

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we get t equals x - 1.

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We can just insert x - 1 into the equation now wherever we see t...

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x - 1 squared is the same as x - 1 times x - 1...

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...which equals x squared - x - x + 1.

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When we add like terms, we get x squared - 2x + 1.

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That value times 3...gives us 3x squared - 6x + 3.

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2 times the quantity x - 1 equals 2x - 2...

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Combining like terms...we have 3x squared - 6x + 2x

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and that gives us - 4x...3 - 2 - 1...gives us 0.

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So we're left with 3x squared - 4x.

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Which is answer choice (C).

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