What is the vertex form of $y = x^{2} - x - 72$ $y=x^2-x-72$ ?

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What is the vertex form of $y = x^{2} - x - 72$ $y=x^2-x-72$ ?

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Answer 1 · 2016-07-24T17:37:32

$y = {(x - \frac{1}{2})}^{2} - 72 \frac{1}{4}$ $y=(x-1/2)^2-72 1/4$

Explanation:

Given

$y = x^{2} - x - 72$ $y=x^2-x-72$

Find the Vertex

X-cordinate of the vertex

$x = \frac{- b}{2 a} = \frac{- (- 1)}{2 \times 1} = \frac{1}{2}$ $x=(-b)/(2a)=(-(-1))/(2xx1)=1/2$
At $x = \frac{1}{2}; y = {(\frac{1}{2})}^{2} - \frac{1}{2} - 72 = \frac{1}{4} - \frac{1}{2} - 72 = - 72 \frac{1}{4}$ $x=1/2; y=(1/2)^2-1/2-72=1/4-1/2-72=-72 1/4$

Vertex for of the quardratic equation is

$y = a (x - h) + k$ $y=a(x-h)+k$

Where $h$ $h$ is $x$ $x$ cordinate and $k$ $k$ is $y$ $y$ coordinate
$a$ $a$ is the coefficient of $x^{2}$ $x^2$

$h = \frac{1}{2}$ $h=1/2$
$k = - 72 \frac{1}{4}$ $k=-72 1/4$
$a = 1$ $a=1$

Substitute these values in the formula

$y = {(x - \frac{1}{2})}^{2} - 72 \frac{1}{4}$ $y=(x-1/2)^2-72 1/4$

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What is the vertex form of $y = x^{2} - x - 72$ $y=x^2-x-72$ ?

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What is the vertex form of y=x2−x−72y=x^2-x-72 ?

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Explanation:

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What is the vertex form of $y = x^{2} - x - 72$ $y=x^2-x-72$ ?