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SAT Math 7.3 Algebra and Functions 318 Views


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SAT Math 7.3 Algebra and Functions

Language:
English Language

Transcript

00:02

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

00:07

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

00:12

Thank goodness.

00:13

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

00:18

then y is also equal to which of the following?

00:21

And here are the potential answers...

00:26

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

00:28

This shows us that we're dealing with something

00:31

called PARAMETRIC equations.

00:33

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

00:41

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

00:45

to solve for y in terms of x.

00:48

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

00:51

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

00:55

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

01:00

we get t equals x - 1.

01:02

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

01:08

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

01:14

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

01:20

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

01:27

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

01:31

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

01:37

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

01:42

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

01:49

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

01:51

Which is answer choice (C).

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