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SAT Math 4.1 Algebra and Functions 1196 Views


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Description:

SAT Math 4.1 Algebra and Functions

Language:
English Language

Transcript

00:02

And here's your mathy shmoop du jour...

00:05

Where do the graphs of y = -1/2 x squared + 4

00:09

and x - 2y = -2 meet?

00:14

And here are the potential answers...

00:20

We actually want to know where the two graphs INTERSECT.

00:22

In other words, we have to solve a system of equations.

00:26

For this problem, the easiest way to do that is by substitution because we already have

00:30

y equals something in one of the equations...

00:33

...and we can just plug in that value of y into the second equation.

00:37

We get x - 2 times the quantity -1/x squared + 4 = -2

00:44

We can distribute the -2 in the parentheses on the left side

00:48

to get x + x squared - 8 = -2.

00:52

Then we add 2 to both sides...to get x squared + x - 6 = 0.

00:59

Our equation factors into x + 3 times x - 2.

01:03

To make the left side equal zero, one of the factors has to be zero, so x equals either

01:09

2 or -3. Let's plug these two solutions into one

01:12

of our original equations to find y.

01:15

We'll go with the first one, since it's already solved for y.

01:18

When x equals 2, y equals -1/2 times 2 squared + four.

01:23

We can multiply the 2 squared by -1/2, and add 4 to get y = 2.

01:28

Next, we can plug in -3 for x, which gives us y = -1/2.

01:34

Our two solutions are (2, 2) and (-3, -1/2).

01:39

Looks like our answer is B.

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