What is the vertex form of $y = x^{2} + 9 x + 3$ $y=x^2+9x+3$ ?

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What is the vertex form of $y = x^{2} + 9 x + 3$ $y=x^2+9x+3$ ?

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Answer 1 · 2018-04-21T14:02:17

$(- \frac{9}{2} ∣ - \frac{69}{4})$ $(-color(red)(9/2)|color(green)(-69/4))$

Explanation:

$y = x^{2} + 9 x + 3$ $y=x^2+9x+3$
$y = x^{2} + 2 \cdot \frac{9}{2} x + {(\frac{9}{2})}^{2} - {(\frac{9}{2})}^{2} + 3$ $y=x^2+2*9/2x+(9/2)^2-(9/2)^2+3$
$y = {(x + \frac{9}{2})}^{2} - \frac{81}{4} + 3$ $y=(x+9/2)^2-81/4+3$
$y = {(x + \frac{9}{2})}^{2} - \frac{69}{4}$ $y=(x+color(red)(9/2))^2color(green)(-69/4)$

The vertex is at $(- \frac{9}{2} ∣ - \frac{69}{4})$ $(-color(red)(9/2)|color(green)(-69/4))$

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What is the vertex form of $y = x^{2} + 9 x + 3$ $y=x^2+9x+3$ ?

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What is the vertex form of $y = x^{2} + 9 x + 3$ $y=x^2+9x+3$ ?