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What is the vertex form of $y = x (x - 7)$ $y= x(x - 7)$ ?

1 Answer

Mar 14, 2016

$y = 1 {(x - \frac{7}{2})}^{2} + (- \frac{49}{4})$ $y=1(x-7/2)^2+(-49/4)$

Explanation:

The general vertex form is
$XXX y = m {(x - a)}^{2} + b$ $color(white)("XXX")y=color(green)(m)(x-color(red)(a))^2+color(blue)(b)$ with vertex at $(a, b)$ $(color(red)(a),color(blue)(b))$

Given
$XXX y = x (x - 7)$ $color(white)("XXX")y=x(x-7)$

$XXX y = x^{2} - 7 x$ $color(white)("XXX")y=x^2-7x$

$XXX y = x^{2} - 7 x + {(\frac{7}{2})}^{2} - {(\frac{7}{2})}^{2}$ $color(white)("XXX")y=x^2-7x+(7/2)^2 - (7/2)^2$

$XXX y = {(x - \frac{7}{2})}^{2} - \frac{49}{4}$ $color(white)("XXX")y=(x-7/2)^2-49/4$

$XXX y = 1 {(x - \frac{7}{2})}^{2} + (- \frac{49}{4})$ $color(white)("XXX")y=color(green)(1)(x-color(red)(7/2))^2+(color(blue)(-49/4))$

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