# What is the standard form of y= (7/5x-4/7)^2+4?

Oct 2, 2017

$y = \frac{49}{25} {x}^{2} - \frac{8}{5} x + \frac{212}{49}$

#### Explanation:

Basically you just expand out the bracket.

Rule for squaring things: the first squared, plus the last squared, plus twice the product of the two. (like if you had ${\left(x + 3\right)}^{2}$ it'd be ${x}^{2} + {3}^{2} + \text{twice} \left(3 \cdot x\right) = {x}^{2} + 6 x + 9$)

So, ${\left(\frac{7}{5} x - \frac{4}{7}\right)}^{2}$ will be ${\left(\frac{7}{5} x\right)}^{2}$ + ${\left(- \frac{4}{7}\right)}^{2}$ + $2 \left(\frac{7}{5} x \cdot - \frac{4}{7}\right)$
$= \frac{49}{25} {x}^{2} + \frac{16}{49} - \frac{8}{5} x$

$= \frac{49}{25} {x}^{2} - \frac{8}{5} x + 4 + \frac{16}{49} = \frac{49}{25} {x}^{2} - \frac{8}{5} x + \frac{212}{49}$