# How do you graph y + 1/2 = -1/3(x+1/2)?

Feb 16, 2016

$y = {x}^{2} / 3 + \frac{x}{3} - \frac{5}{12}$

#### Explanation:

You need to transform the given equation into a more workable format.

Subtract $\textcolor{b l u e}{\frac{1}{2}}$ from both sides.

$y + \frac{1}{2} \textcolor{b l u e}{- \frac{1}{2}} = - \frac{1}{3} {\left(x + \frac{1}{2}\right)}^{2} \textcolor{b l u e}{- \frac{1}{2}}$

$y + 0 = \frac{1}{3} {\left(x + \frac{1}{2}\right)}^{2} - \frac{1}{2}$
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Square the brackets

$y = \frac{1}{3} \left({x}^{2} + x + \frac{1}{4}\right) - \frac{1}{2}$

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Multiply the contents of the brackets by $\frac{1}{3}$

$y = \frac{{x}^{2}}{3} + \frac{x}{3} + \frac{1}{12} - \frac{1}{2}$

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Simplify the constant

$y = {x}^{2} / 3 + \frac{x}{3} - \frac{5}{12}$
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Produce a table of values and plot your graph