# How do you write the quadratic function in standard form y=2/3(x-9)^2-4?

Jul 9, 2018

$y = \frac{2}{3} {x}^{2} - 12 x + 50$

#### Explanation:

Given: $y = \frac{2}{3} {\left(x - 9\right)}^{2} - 4$

Distribute using ${\left(a + b\right)}^{2} = {a}^{2} + 2 a b + {b}^{2}$

$y = \frac{2}{3} \left({x}^{2} - 18 x + 81\right) - 4$

$y = \frac{2}{3} {x}^{2} - \frac{2}{3} \cdot \frac{18}{1} x + \frac{2}{3} \cdot \frac{81}{1} - 4$

$y = \frac{2}{3} {x}^{2} - 12 x + 54 - 4$

$y = \frac{2}{3} {x}^{2} - 12 x + 50$