How do you write $y = 2 x^{2} - 12 x + 11$ $y = 2x^2-12x+11$ into vertex form?

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How do you write $y = 2 x^{2} - 12 x + 11$ $y = 2x^2-12x+11$ into vertex form?

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Answer 1 · 2015-05-29T13:31:32

The general vertex form for a quadratic is
$y = m (x - a) + b$ $y = m(x-a)+b$ where $(a, b)$ $(a,b)$ is the vertex.

$y = 2 x^{2} - 12 x + 11$ $y=2x^2-12x+11$
$XXXX$ $color(white)("XXXX")$ extract the $m$ $m$
$y = 2 (x^{2} - 6 x) + 11$ $y=2(x^2-6x) +11$
$XXXX$ $color(white)("XXXX")$ complete the square
$y = 2 (x^{2} - 6 x + 9) + 11 - 18$ $y=2(x^2-6x+9) +11 -18$
$XXXX$ $color(white)("XXXX")$ simplify to vertex form
$y = 2 {(x - 3)}^{2} + (- 7)$ $y=2(x-3)^2 + (-7)$
$XXXX$ $color(white)("XXXX")$ with the vertex at $(3, - 7)$ $(3,-7)$

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How do you write $y = 2 x^{2} - 12 x + 11$ $y = 2x^2-12x+11$ into vertex form?

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How do you write y=2x2−12x+11y = 2x^2-12x+11 into vertex form?

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How do you write $y = 2 x^{2} - 12 x + 11$ $y = 2x^2-12x+11$ into vertex form?