ShmoopTube

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And here is your shmoop du jour...

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What shape is shown by the equation X -4 equals the quantity y plus 2 squared?

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And here are the potential answers...

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The key to this problem is knowing the standard equations of all of the

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context in the list

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First we can eliminate C, triangle from our options, because a

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triangle cannot be shown by one equation

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it's made up of three lines. Alright let's move back to A

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Circle, the standard formula of a circle is

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R-squared equals quantity X minus H squared plus quantity Y minus K

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squared where R is the radius

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HK is the center of the circle

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The circle formula has X and Y radius to the second power

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but our equation only raises one variable Y

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to the second power. So we can cross A off our list.

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Next up B. Ellipse, while the formula

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of an ellipse is quantity X minus H square divided by

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A squared plus quantity Y minus K squared

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divided by B squared equals one where HK is the center

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and A is half the length of the major axis

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and B is half of the minor axis...well

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does that look like our equation? No! Cross off B.

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Next up, D, Parabola.

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The equation of an up or down parabola

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is Y minus K equals quanitiy

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X minus H squared. Does that look like our equation? Well...

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...Close but not quite, but wait what about those

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sideways parabolas? Well the equation of a sideways parabola is

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X minus H equals quantity Y minus K squared

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and our equation is X minus 4 equals quanity Y plus 2 squared

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Is that a match? Yeah! In our sideways parabola

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H is 4 and K is negative 2. Got our answer.

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D...Parabola

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