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SAT Math 7.3 Algebra and Functions 318 Views
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Description:
SAT Math 7.3 Algebra and Functions
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?
Full Transcript
- 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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