How do you find the VERTEX of a parabola $y = - 3 x^{2} + 12 x - 9$ $y=-3x^2+12x-9$ ?

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How do you find the VERTEX of a parabola $y = - 3 x^{2} + 12 x - 9$ $y=-3x^2+12x-9$ ?

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Answer 1 · 2015-07-22T12:14:32

Re-write the given equation in "vertex form" to get:
$XXXX$ $color(white)("XXXX")$ vertex at $(2, 3)$ $(2,3)$

Explanation:

The general "vertex form" for a parabola is
$XXXX$ $color(white)("XXXX")$ $y = m {(x - a)}^{2} + b$ $y=m(x-a)^2+b$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ with a vertex at $(a, b)$ $(a,b)$

Given $y = - 3 x^{2} + 12 x - 9$ $y = -3x^2+12x-9$

Extract $m$ $m$
$XXXX$ $color(white)("XXXX")$ $y = (- 3) (x^{2} - 4 x) - 9$ $y = (-3)(x^2-4x) -9$

Complete the square:
$XXXX$ $color(white)("XXXX")$ $y = (- 3) (x^{2} - 4 x + 4) - 9 + 3 (4)$ $y = (-3)(x^2-4x+4) - 9 +3(4)$

$XXXX$ $color(white)("XXXX")$ $y = (- 3) {(x - 2)}^{2} + 3$ $y = (-3)(x-2)^2 +3$
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ which is the vertex form
$XXXX$ $color(white)("XXXX")$ $XXXX$ $color(white)("XXXX")$ with vertex at $(2, 3)$ $(2,3)$

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How do you find the VERTEX of a parabola $y = - 3 x^{2} + 12 x - 9$ $y=-3x^2+12x-9$ ?

1 Answer

Explanation:

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Science

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How do you find the VERTEX of a parabola y=−3x2+12x−9y=-3x^2+12x-9?

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Explanation:

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How do you find the VERTEX of a parabola $y = - 3 x^{2} + 12 x - 9$ $y=-3x^2+12x-9$ ?