# What is the vertex form of y= 5x^2-2x – 6 ?

Jul 29, 2016

See explanation

#### Explanation:

$\textcolor{b l u e}{\text{Step 1}}$

Write as: $y = 5 \left({x}^{2} - \frac{2}{5} x\right) - 6 + k$

where $k$ is a correction for an error that will be introduced by the method.
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$\textcolor{b l u e}{\text{Step 2}}$
$\textcolor{b r o w n}{\text{Move the power to outside the brackets}}$

$y = 5 {\left(x - \frac{2}{5} x\right)}^{2} - 6 + k$
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$\textcolor{b l u e}{\text{Step 3}}$
$\textcolor{b r o w n}{\text{Halve the } \frac{2}{5}}$

$y = 5 {\left(x - \frac{2}{10} x\right)}^{2} - 6 + k$
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$\textcolor{b l u e}{\text{Step 4}}$
$\textcolor{b r o w n}{\text{Remove the "x" from } - \frac{2}{10} x}$

$y = 5 {\left(x - \frac{2}{10}\right)}^{2} - 6 + k$

$\textcolor{g r e e n}{\text{Now we need to determine the value of } k}$
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$\textcolor{b l u e}{\text{Step 5}}$

The squaring the $- \frac{2}{10} \text{ } \to + \frac{4}{100}$

Now multiply it by the 5 $\to 5 \times \frac{4}{100} = \frac{4}{20} \equiv \frac{1}{5}$

So $\frac{1}{5} + k = 0 \implies k = - \frac{1}{5}$ giving

$\text{ } \textcolor{p u r p \le}{\overline{\underline{| \textcolor{w h i t e}{\frac{\frac{2}{2}}{2}} y = 5 {\left(x - \frac{1}{5}\right)}^{2} - \frac{31}{5} \textcolor{w h i t e}{\frac{2}{2}} |}}}$

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$\textcolor{w h i t e}{.}$