# How do you write the function in standard form y=2(x-1)(x-6)?

May 24, 2018

$y = 2 {x}^{2} - 14 x + 12$

#### Explanation:

Standard form of a quadratic takes the shape $a {x}^{2} + b x + c = 0$. This usually comes about from an expansion of the expression $\left(\alpha x + \beta\right) \left(\gamma x + \delta\right)$, using the distributive property such that $\left(a + b\right) \left(c + d\right) = a c + a d + b c + b d$.

Using these rules, we now expand the expression
$y = \left(2\right) \left(x - 1\right) \left(x - 6\right)$ by first multiplying the first two brackets, to get
$y = \left(2 \cdot x + 2 \cdot - 1\right) \left(x - 6\right) = \left(2 x - 2\right) \left(x - 6\right)$. Next we expand the last two brackets, to get
$y = 2 x \cdot x + 2 x \cdot \left(- 6\right) + \left(- 2\right) \cdot x + \left(- 2\right) \cdot \left(- 6\right)$ $= 2 {x}^{2} - 12 x - 2 x + 12$
Lastly we simplify by grouping like terms, to get
$y = 2 {x}^{2} - 14 x + 12$, the answer.

I hope that helped!