# What is the standard form of y= (3/2x-4)^2+1?

Jul 14, 2018

$y = \frac{9}{4} {x}^{2} - 12 x + 17$

#### Explanation:

"the standard form of a quadratic is ";ax^2+bx+c;a!=0

$\text{to obtain this form expand and collect like terms}$

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

$\textcolor{w h i t e}{y} = \frac{9}{4} {x}^{2} - 6 x - 6 x + 16 + 1$

$\textcolor{w h i t e}{y} = \frac{9}{4} {x}^{2} - 12 x + 17 \leftarrow \textcolor{red}{\text{in standard form}}$