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SAT Math 8.6 Algebra and Functions 231 Views


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SAT Math 8.6 Algebra and Functions

Language:
English Language

Transcript

00:03

It's a bird! It's a plane! It's Shmooperman...guy!

00:09

Find the positive x-coordinate of the point where the graphs of the equations…

00:14

y = -2x squared - 6 y = -3x - 8 …intersect.

00:22

Okay…so this question is asking us to solve for two linear equations.

00:28

So, back in our old algebra days, we knew we had several methods that could help us do this…

00:33

Solving by substitution…

00:35

…solving by elimination…

00:36

…or solving by graphing.

00:38

So in this case we can do any of these, but the easiest would be to just set them equal,

00:42

because…y equals y.

00:44

So we have -2x squared – 6 equals -3x – 8.

00:50

Now combine like terms and move everything to one side and we get:

00:54

2x squared – 3x – 2 = 0

00:59

…and that looks like a FACTORABLE quadratic equation.

01:03

Easiest way to solve this equation is to factor by grouping.

01:07

So if we split our -3x into x and -4x...

01:12

...we get 2x squared + x - 4x - 2 = 0.

01:19

This whole thing factors into x(2x + 1) - 2(2x + 1) = 0

01:27

Now we both have x and -2 multiplied by the quantity 2x + 1.

01:31

Do you know what we have to do next?

01:33

Factor out that 2x + 1.

01:36

Our final, fully factored equation is (2x + 1)(x-2) = 0.

01:44

Well, when x = -1/2 and 2... this equation is true.

01:48

Since the question asks for the positive x-coordinate, we'll take the positive 2.

01:54

So the answer is…2. That’s where they intersect.

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