What is the vertex of $y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$ ? (This replaces the same question that I accidentally deleted before my first cup of coffee).

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What is the vertex of $y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$ ? (This replaces the same question that I accidentally deleted before my first cup of coffee).

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Answer 1 · 2015-06-29T11:09:29

The vertex of $- x^{2} + 4 x + 12$ $-x^2+4x+12$ is at $(2, 16)$ $(2,16)$

Explanation:

By rewriting $y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$
into "vertex form": $y = m {(x - a)}^{2} + b$ $y=m(x-a)^2+b$ (with vertex at $(a, b)$ $(a,b)$ )
we can simply "read off" the vertex values.

$y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$
$XXXX$ $color(white)("XXXX")$ extract $m$ $m$
$y = (- 1) (x^{2} - 4 x - 12)$ $y=(-1)(x^2-4x-12)$
$XXXX$ $color(white)("XXXX")$ complete the square
$y = (- 1) (x^{2} - 4 x + 4 - 12 - 4)$ $y=(-1)(color(blue)(x^2-4x+4) -12 -4)$
$XXXX$ $color(white)("XXXX")$ rewrite as a square plus an external term
$y = (- 1) {(x - 2)}^{2} + 16$ $y=(-1)(x-2)^2 +16$

This is in vertex form with the vertex at $(2, 16)$ $(2,16)$

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What is the vertex of $y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$ ? (This replaces the same question that I accidentally deleted before my first cup of coffee).

1 Answer

Explanation:

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Science

Math

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What is the vertex of y=−x2+4x+12y=-x^2+4x+12? (This replaces the same question that I accidentally deleted before my first cup of coffee).

1 Answer

Explanation:

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Impact of this question

What is the vertex of $y = - x^{2} + 4 x + 12$ $y=-x^2+4x+12$ ? (This replaces the same question that I accidentally deleted before my first cup of coffee).