ShmoopTube

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For a good time, solve this shmoopy question.

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Find the vertex of the parabola  y = 2x squared -- 4x + 1.

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And here are your potential answers...

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...do we know the standard form formula?

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Well, if we were in class that day... ahem...we'd know that its form is:

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y = a(x -- h) squared + k.... where the vertex is (h,k)

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The k is gonna be all about how high or low the vertex of the parabola sits along the y

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axis direction.

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A vertex is this base point on the parabola.... its absolute bottom or top or... side thing.

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So now we have this equation that they give us:

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and we have to put it into standard form.

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We can first subtract 1 from both sides and then factor out the 2 on the right to get

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y minus 1 equals 2 times quantity x squared minus 2x.

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We can now complete the square inside the parentheses...

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Given x squared plus bx...we can

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complete the square by adding the quantity b over 2 squared...

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In this case, when we look at x squared minus 2x in the parentheses...b is negative 2..so

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negative 2 divided by 2 is negative 1...and negative 1 squared is 1.

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But remember, we've just completed the square in the parentheses...so we're actually adding

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2 to the right side...which means we have to add 2 to the left side as well.

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The right side simplifies to 2 times the quantity x minus 1 squared...and the left side simplifies

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to y plus 1. We can now subtract 1 from both sides... and we see that the equation is in standard form!

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We see that h is 1 and k is negative 1. So our vertex is (1, -1).

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Answer's (B).

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