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00:02

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

00:05

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

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and x - 2y = -2 meet?

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And here are the potential answers...

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We actually want to know where the two graphs INTERSECT.

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

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

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y equals something in one of the equations...

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

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

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

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

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

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

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

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

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of our original equations to find y.

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

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

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

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

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

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Looks like our answer is B.

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