# What is the vertex form of y=9x^2-48x+64 ?

Feb 27, 2017

You can see a more in-depth build approach example at https://socratic.org/s/aCybisPL

$y = 9 {\left(x - \frac{8}{3}\right)}^{2}$

#### Explanation:

$\textcolor{b l u e}{\text{Preamble}}$

If you can do so it is worth committing to memory the standardised form.

Using $y = a {x}^{2} + b x + c$ as the bases we have the vertex form format of:

$y = a {\left(x + \frac{b}{2 a}\right)}^{2} + k + c$

The extra $k$ is a correction that 'gets rid' if the error introduced by squaring the $+ \frac{b}{2 a}$ part of ${\left(x + \frac{b}{2 a}\right)}^{2}$
The ${\left(\frac{b}{2 a}\right)}^{2}$ part is not in the original equation.

Do not forget about the whole bracket being multiplied by a
So to get rid of it we set: $\text{ } a {\left(\frac{b}{2 a}\right)}^{2} + k = 0$
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$\textcolor{b l u e}{\text{Building the vertex form}}$

Write as $y = 9 {\left(x - \frac{48}{2 \left(9\right)}\right)}^{2} + k + 64$

$9 {\left(- \frac{48}{18}\right)}^{2} + k = 0$

$k = - 64$

Thus we have

$y = 9 {\left(x - \frac{8}{3}\right)}^{2} - 64 + 64$

$y = 9 {\left(x - \frac{8}{3}\right)}^{2}$